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  • 51.
    Dyrssen, Hannah
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Ekström, Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Tysk, Johan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Pricing equations in jump-to-default models2014Inngår i: International Journal of Theoretical and Applied Finance, ISSN 0219-0249Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study pricing equations in jump-to-default models, and we provide conditions under which the option price is the unique classical solution, with a special focus on boundary conditions. In particular, we find precise conditions ensuring that the option price at the default boundary coincides with the recovery payment. We also study spatial convexity of the option price, and we explore the connection between preservation of convexity and parameter monotonicity.

  • 52.
    Dyrssen, Hannah
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Vannestål, Martin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Optimal stopping games for a process with jumpsArtikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    This paper presents a study of a general two-player optimal stopping game in a jump-diffusion model. An iterative scheme to find the value of this game is derived, specifically the value is shown to be the limit of a sequence of stopping games for a related diffusion but with a running reward. Furthermore the convergence is uniform and exponential. The special case of a cancellable put option is studied.

  • 53.
    Dyrssen, Hannah
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Vannestål, Martin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    The integral equation for the American put boundary in models with jumpsArtikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    The price of the American put option is frequently studied as the solution to an associated free-boundary problem. This free boundary, the optimal exercise boundary, determines the value of the option. In spectrally negative models the early exercise premium representation for the value of the option gives rise to an integral equation for the boundary. We study this integral equation and prove that the optimal exercise boundary is the unique solution and thus that the equation characterizes the free boundary. In a spectrally positive model, this approach does not give an equation for the boundary. We instead find lower and upper bounds for the true boundary which can be found by solving related equations.

  • 54.
    Eggers, Julia
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    On Statistical Methods for Zero-Inflated Models2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 55.
    Ekholm, Maria
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Modellering av olyckors påverkan på en järnvägsanläggnings driftsäkerhet och livscykelkostnad2019Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [en]

    One of the challenges for the railroad system to be able to be competitive, are the delays and how to reduce these delays. Therefore, it is important to look over the cost of accidents for the whole society. Accidents, involving humans and animals constitutes a lot of delays today, which impacts the whole railroad system, even far away from where the accident took place. In this study, delays have been investigated with the help of regression analysis. The purpose has been to evaluate time and cost for society of accidents involving humans and animals. The study has been conducted with a life-cycle-cost and reliability perspective. The approximated value of delay time for an accident involving humans has been set to 306 minutes, and to 18 minutes involving animals. It also showed that the time of the year doesn´t impact on how many minutes the train will be delayed if an accident occurs. Also, it would be interesting to investigate further different places and what can be done in specific places that suffer from a high number of delays to be able to improve the Swedish railroad even further. With the help of a calculation model, it has been calculated that accidents cost billions a year for the society. In the study, persons of interest at Trafikverket have been interviewed, and it shows that today's work with accidents manly targets what to do when an accident already has occurred, such as evacuating.

  • 56.
    Ekström, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Janson, Svante
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    The inverse first-passage problem and optimal stopping2016Inngår i: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 26, nr 5, s. 3154-3177Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Given a survival distribution on the positive half-axis and a Brownian motion, a solution of the inverse first-passage problem consists of a boundary so that the first passage time over the boundary has the given distribution. We show that the solution of the inverse first-passage problem coincides with the solution of a related optimal stopping problem. Consequently, methods from optimal stopping theory may be applied in the study of the inverse first passage problem. We illustrate this with a study of the associated integral equation for the boundary.

  • 57.
    Ekström, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Tysk, Johan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Comparison of two methods for superreplication2012Inngår i: Applied Mathematical Finance, ISSN 1350-486X, E-ISSN 1433-4313Artikkel i tidsskrift (Fagfellevurdert)
  • 58.
    Ekström, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Tysk, Johan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Dupire's equation for bubbles2012Inngår i: International Journal of Theoretical and Applied Finance, ISSN 0219-0249Artikkel i tidsskrift (Fagfellevurdert)
  • 59.
    Ekström, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Tysk, Johan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Lindberg, Carl
    Optimal liquidation of a pairs trade2011Inngår i: Advanced Mathematical Methods in Finance, Springer-Verlag New York, 2011Kapittel i bok, del av antologi (Fagfellevurdert)
  • 60.
    Ekström, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Vaicenavicius, Juozas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Optimal liquidation of an asset under drift uncertainty2016Inngår i: SIAM Journal on Financial Mathematics, ISSN 1945-497X, E-ISSN 1945-497XArtikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift by allowing an arbitrary probability distribution to characterize the uncertainty about the drift parameter. Filtering theory is used to describe the evolution of the posterior beliefs about the drift once the price process is being observed. An optimal stopping time is determined as the first passage time of the posterior mean below a monotone boundary, which can be characterized as the unique solution to a nonlinear integral equation. We also study monotonicity properties with respect to the prior distribution and the asset volatility.

  • 61.
    Ekström, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Vaicenavicius, Juozas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Optimal stopping of a Brownian bridge with an unknown pinning pointArtikkel i tidsskrift (Annet vitenskapelig)
  • 62.
    Ekström, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Vaicenavicius, Juozas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Wiener disorder detection under disorder magnitude uncertaintyManuskript (preprint) (Annet vitenskapelig)
  • 63.
    Ekström, Erik
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Vannestål, Martin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    Momentum liquidation under partial information2016Inngår i: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, nr 2, s. 341-359Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Momentum is the notion that an asset that has performed well in the past will continue to do so for some period. We study the optimal liquidation strategy for a momentum trade in a setting where the drift of the asset drops from a high value to a smaller one at some random change-point. This change-point is not directly observable for the trader, but it is partially observable in the sense that it coincides with one of the jump times of some exogenous Poisson process representing external shocks, and these jump times are assumed to be observable. Comparisons with existing results for momentum trading under incomplete information show that the assumption that the disappearance of the momentum effect is triggered by observable external shocks significantly improves the optimal strategy.

  • 64.
    Enciso, Alberto
    et al.
    CSIC, Inst Ciencias Matemat, Madrid 28049, Spain.
    Luque, Alejandro
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Peralta-Salas, Daniel
    CSIC, Inst Ciencias Matemat, Madrid 28049, Spain.
    Stationary Phase Methods and the Splitting of Separatrices2019Inngår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 368, nr 3, s. 1297-1322Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Using stationary phase methods, we provide an explicit formula for the Melnikov function of the one and a half degrees of freedom system given by a Hamiltonian system subject to a rapidly oscillating perturbation. Remarkably, the Melnikov function turns out to be computable using very little information on the separatrix and in the case of non-analytic systems. This is related to a priori stable systems coupled with low regularity perturbations. A natural physical application is to perturbations controlled by wave-type equations, so in particular we also illustrate this result with the motion of charged particles in a rapidly oscillating electromagnetic field. Quasi-periodic perturbations are discussed too.

  • 65.
    Eriksson, Linnéa
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    PSA testing, seasonal variation and relations to media in terms of prostate cancer2019Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 66.
    Eriksson, Olle
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Modeling Information Transfer in High-Density Crowds2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 67.
    Falk Soylu, Denniz
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Dimension Reduction Methods for Predicting Financial Data2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 68.
    Falk Soylu, Denniz
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Recovery Rate Modelling of Non-performing Consumer Loans2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 69.
    Fastlund, Niklas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    To learn and evaluate a system for recommending business intentions based on customer behaviour2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 70.
    Fellström, Bengt
    et al.
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för medicinska vetenskaper.
    Helmersson-Karlqvist, Johanna
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för medicinska vetenskaper.
    Lind, Lars
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för medicinska vetenskaper.
    Soveri, Inga
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för medicinska vetenskaper.
    Wu, Ping-Hsun
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för medicinska vetenskaper.
    Thulin, Måns
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Ärnlöv, Johan
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska och farmaceutiska vetenskapsområdet, centrumbildningar mm, Centrum för klinisk forskning Dalarna.
    Larsson, Anders
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för medicinska vetenskaper.
    Associations Between Apolipoprotein A1, High-Density Lipoprotein Cholesterol, and Urinary Cytokine Levels in Elderly Males and Females.2019Inngår i: Journal of Interferon and Cytokine Research, ISSN 1079-9907, E-ISSN 1557-7465Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    There exists a close relationship between cardiovascular diseases and chronic kidney disease. Apolipoprotein A1 and high-density lipoprotein (HDL) cholesterol are widely used as cardiovascular risk markers but they also have anti-inflammatory properties. The aim of this study was to investigate any associations between HDL levels and cytokine levels in urine. We randomly selected 90 urine samples from the Prospective Investigation of the Vasculature in Uppsala Seniors Study (41 males and 49 females). The samples were analyzed with 2 multiplex assays, Multiplex Inflammation I and Cardiovascular II kits (Olink Bioscience, Uppsala, Sweden). We analyzed the correlations between 158 cytokines in urine with apolipoprotein A1, HDL cholesterol, apolipoprotein B, and low-density lipoprotein cholesterol. There were strong correlations for apolipoprotein A1 and HDL cholesterol with individual cytokines. After adjustment for multiplicity testing, there were 33 significant correlations between apolipoprotein A1 and cytokine levels and 14 of these were also significantly correlated with HDL cholesterol. The strongest associations were observed for IL-1α, SPON2, RAGE, PAR-1, TRAIL-R2, IL-4RA, TNFRSF11A, and SCF. A total of 28 out of 33 correlations were negative, indicating a negative relationship between apolipoprotein A1 and urinary cytokines. The study shows a negative correlation between apolipoprotein A1 and HDL cholesterol and urinary cytokine levels. The finding is in agreement with the anti-inflammatory properties of HDL.

  • 71.
    Figueras, Jordi-Lluis
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Haro, A.
    Univ Barcelona, Dept Matemat Aplicada & Anal, Gran Via 585, E-08007 Barcelona, Spain..
    Luque, A.
    CSIC, Inst Ciencias Matemat, C Nicolas Cabrera 13-15, Madrid 28049, Spain..
    Rigorous Computer-Assisted Application of KAM Theory: A Modern Approach2017Inngår i: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383, Vol. 17, nr 5, s. 1123-1193Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we present and illustrate a general methodology to apply KAM theory in particular problems, based on an a posteriori approach. We focus on the existence of real analytic quasi-periodic Lagrangian invariant tori for symplectic maps. The purpose is to verify the hypotheses of a KAM theorem in an a posteriori format: Given a parameterization of an approximately invariant torus, we have to check non-resonance (Diophantine) conditions, non-degeneracy conditions and certain inequalities to hold. To check such inequalities, we require to control the analytic norm of some functions that depend on the map, the ambient structure and the parameterization. To this end, we propose an efficient computer-assisted methodology, using fast Fourier transform, having the same asymptotic cost of using the parameterization method for obtaining numerical approximations of invariant tori. We illustrate our methodology by proving the existence of invariant curves for the standard map (up to ), meandering curves for the non-twist standard map and 2-dimensional tori for the Froeschl, map.

  • 72.
    Figueras, Jordi-Lluis
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Haro, Alex
    Univ Barcelona, Dept Matemat Aplicada & Anal, Gran Via 585, E-08007 Barcelona, Spain..
    A note on the fractalization of saddle invariant curves in quasiperiodic systems2016Inngår i: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 9, nr 4, s. 1095-1107Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The purpose of this paper is to describe a new mechanism of destruction of saddle invariant curves in quasiperiodically forced systems, in which an invariant curve experiments a process of fractalization, that is, the curve gets increasingly wrinkled until it breaks down. The phenomenon resembles the one described for attracting invariant curves in a number of quasiperiodically forced dissipative systems, and that has received the attention in the literature for its connections with the so-called Strange Non-Chaotic Attractors. We present a general conceptual framework that provides a simple unifying mathematical picture for fractalization routes in dissipative and conservative systems.

  • 73.
    Figueras, Jordi-Lluis
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Haro, Alex
    Universitat de Barcelona, Departament de Matemàtiques i Informàtica.
    Luque, Alejandro
    Consejo Superior de Investigaciones Científicas, CSIC, Instituto de Ciencias Matemáticas.
    On the sharpness of the Rüssmann estimates2018Inngår i: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 55, s. 42-55Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Estimating the norm of the solution of the linear difference equation u (theta) - u (theta + omega) = v (theta) plays a fundamental role in KAM theory. Optimal (in certain sense) estimates for the solution of this equation were provided by Russmann in the mid 70's. The aim of this paper is to compare the sharpness of these classical estimates with more specific estimates obtained with the help of the computer. We perform several experiments to quantify the improvement obtained when using computer assisted estimates. By comparing these estimates with the actual norm of the solution, we can analyze the different sources of overestimation, thus encouraging future improvements.

  • 74.
    Figueras, Jordi-Lluis
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Lilja, Dan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Existence of non-smooth bifurcations of uniformly hyperbolic invariant manifolds in skew product systems2018Inngår i: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 31, nr 12, s. 5573-5588Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we study the anti-integrable limit scenario of skew product systems. We consider a generalization of such systems based on the Frenkel-Kontorova model, and prove that under certain mild regularity conditions on the potential the structure of the orbits is of Cantor type. From our results we deduce the existence of the non-smooth folding bifurcation (conjectured by Figueras and Haro (2015 Chaos 25 123119)). Lastly we present some results which are useful in determining if a potential satisfies the regularity conditions required for the Cantor sets of orbits to exist and are also of independent interest. We also prove the existence of orbits with any fibered rotation number in systems of both one and two degrees of freedom. In particular, our results also apply to two-dimensional maps with degenerate potentials (vanishing second derivative), so extending the results of existence of Cantori to more general twist maps.

  • 75.
    Fraile, Marc
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    A study of an approximate equation for sharp fronts in the generalized Surface Quasi-Geostrophic Equations in the cylinder2019Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 76.
    Fredriksson, Teodor
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Fokker Planck for the Cox-Ingersoll-Ross Model2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 77.
    Frisk, Martin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Synchronization in chaotic dynamical systems2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 78.
    Fröberg, Malvina
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Optimal Importance Sampling for Diffusion Processes2019Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 79.
    Fröberg, Malvina
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Testing for Structural Change in Regression Models of Meat Consumption in Sweden2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 80.
    Gaidashev, Denis
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    On the Scaling Ratios for Siegel Disks2015Inngår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 333, nr 2, s. 931-957Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point and the rotation number whose continued fraction expansion is preperiodic has been observed to be self-similar with a certain scaling ratio. The restriction of the dynamics of the quadratic polynomial to the boundary of the Siegel disk is known to be quasisymmetrically conjugate to the rigid rotation with the same rotation number. The geometry of this self-similarity is universal for a large class of holomorphic maps. A renormalization explanation of this universality has been proposed in the literature. In this paper we provide an estimate on the quasisymmetric constant of the conjugacy, and use it to prove bounds on the scaling ratio lambda of the form alpha(gamma) <= |lambda| <= C delta(s), where s is the period of the continued fraction, and alpha is an element of (0, 1) depends on the rotation number in an explicit way, while C > 1, delta is an element of (0, 1) and gamma is an element of (0, 1) depend only on the maximum of the integers in the continued fraction expansion of the rotation number.

  • 81.
    Gaidashev, Denis
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Renormalization for Lorenz maps of monotone combinatorial types2019Inngår i: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 39, nr 1, s. 132-158Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Lorenz maps are maps of the unit interval with one critical point of order rho > 1 and a discontinuity at that point. They appear as return maps of sections of the geometric Lorenz flow. We construct real a priori bounds for renormalizable Lorenz maps with certain monotone combinatorics and a sufficiently flat critical point, and use these bounds to show existence of periodic points of renormalization, as well as existence of Cantor attractors for dynamics of infinitely renormalizable Lorenz maps.

  • 82.
    Gaidashev, Denis
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Johnson, T.
    Chalmers, Fraunhofer Chalmers Res Ctr Ind Math, S-41296 Gothenburg, Sweden..
    Martens, M.
    SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 USA..
    Rigidity For Infinitely Renormalizable Area-Preserving Maps2016Inngår i: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 165, nr 1, s. 129-159Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The period-doubling Cantor sets of strongly dissipative Henon-like maps with different average Jacobian are not smoothly conjugated, as was shown previously. The Jacobian rigidity conjecture says that the period-doubling Cantor sets of two-dimensional Henon-like maps with the same average Jacobian are smoothly conjugated. This conjecture is true for average Jacobian zero, for example, the one-dimensional case. The other extreme case is when the maps preserve area, for example, when the average Jacobian is one. Indeed, the main result presented here is that the period-doubling Cantor sets of area-preserving maps in the universality class of the Eckmann-Koch-Wittwer renormalization fixed point are smoothly conjugated.

  • 83.
    Gaidashev, Denis
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Johnson, Tomas
    Fraunhofer Chalmers Res Ctr Ind Math, SE-41288 Gothenburg, Sweden..
    Spectral Properties Of Renormalization For Area-Preserving Maps2016Inngår i: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 36, nr 7, s. 3651-3675Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Area-preserving maps have been observed to undergo a universal period-doubling cascade, analogous to the famous Feigenbaum-Coullet-Tresser period doubling cascade in one-dimensional dynamics. A renormalization approach has been used by Eckmann, Koch and Wittwer in a computer-assisted proof of existence of a conservative renormalization fixed point. Furthermore, it has been shown by Gaidashev, Johnson and Martens that infinitely renormalizable maps in a neighborhood of this fixed point admit invariant Cantor sets with vanishing Lyapunov exponents on which dynamics for any two maps is smoothly conjugate. This rigidity is a consequence of an interplay between the decay of geometry and the convergence rate of renormalization towards the fixed point. In this paper we prove a result which is crucial for a demonstration of rigidity: that an upper bound on this convergence rate of renormalizations of infinitely renormalizable maps is sufficiently small.

  • 84.
    Gaidashev, Denis
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Zabzina, Natalia
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Fractal dimentions of the conformal diffusion-limited aggregationManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Diffusion-limited aggregation (DLA) is an important and popular mathematical model of random cluster growth. Conformal DLA, in which a cluster is grown by successive applications of conformal maps, is relletavily new and unexplored version of DLA. We implement conformal DLA numerically and compute several fractal dimentions of DLA clusters. To test applicability of the model to biological systems, the dimentions are compared with the experimentally computed fractal dimentions of the slime mould Physarum Polycephalum.

  • 85. Galias, Zbigniew
    et al.
    Tucker, Warwick
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Is the Hénon attractor chaotic?2015Inngår i: Chaos, ISSN 1054-1500, E-ISSN 1089-7682, Vol. 25, nr 3, artikkel-id 033102Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    By performing a systematic study of the Henon map, we find low-period sinks for parameter values extremely close to the classical ones. This raises the question whether or not the well-known Henon attractor-the attractor of the Henon map existing for the classical parameter values-is a strange attractor, or simply a stable periodic orbit. Using results from our study, we conclude that even if the latter were true, it would be practically impossible to establish this by computing trajectories of the map.

  • 86.
    Galias, Zbigniew
    et al.
    AGH Univ Sci & Technol, Dept Elect Engn, Al Mickiewicza 30, PL-30059 Krakow, Poland.
    Tucker, Warwick
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    On the Existence of the Double Scroll Attractor for the Chua's Circuit with a Smooth Nonlinearity2018Inngår i: 2018 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS (ISCAS), IEEE , 2018Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In simulations of the Chua's circuit with a smooth nonlinearity for certain parameter values one observes the double scroll attractor. This attractor contains an unstable equilibrium, and typical trajectories belonging to the attractor may pass arbitrarily close to this equilibrium. In consequence, it is impossible to compute trajectories over the whole attractor using standard rigorous numerical integration procedures. This is due to the existence of trajectories which spend arbitrarily long time in a neighborhood of the equilibrium. In this work, a method to find enclosures of trajectories passing arbitrarily close to an unstable fixed point of spiral type is presented. This method is used to prove the existence of a trapping region enclosing the double scroll attractor for the Chua's circuit with a cubic nonlinearity.

  • 87. Gaudreau, Philippe
    et al.
    Hayami, Ken
    Aoki, Yasunori
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Farmaceutiska fakulteten, Institutionen för farmaceutisk biovetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Safouhi, Hassan
    Konagaya, Akihiko
    Improvements to the cluster Newton method for underdetermined inverse problems2015Inngår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 283, s. 122-141Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Cluster Newton method (CN method) has proved to be very efficient at finding multiple solutions to underdetermined inverse problems. In the case of pharmacokinetics, underdetermined inverse problems are often given extra constraints to restrain the variety of solutions. In this paper, we propose a new algorithm based on the two parameters of the Beta distribution for finding a family of solutions which best fit the extra constraints. This allows for a much greater control on the variety of solutions that can be obtained with the CN method. In addition, this algorithm facilitates the task of obtaining pharmacologically feasible parameters. Moreover, we also make some improvements to the original CN method including an adaptive margin of error for the perturbation of the target values and the use of an analytical Jacobian in the resolution of the forward problem.

  • 88.
    Gauffin, Oskar
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Prediction of retention time2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 89.
    Gladitz, Johannes
    et al.
    Stat Serv, Berlin, Germany..
    Nussbaum, Michael
    Cornell Univ, Dept Math, Ithaca, NY 14853 USA..
    Zwanzig, Silvelyn
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Biographical item: Obituary for Helga Bunke (13 July 1938-4 May 2014) in Statistics (Berlin), vol 49, issue 6, pp 1187-11882015Annet (Annet (populærvitenskap, debatt, mm))
  • 90.
    Gombrii, David
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Mätning av partiklar (PM10) och buller kring bullerplank och innergårdar: och hur dessa kan skydda boende och gångtrafikanter2015Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [en]

    In this study, atmospheric particle concentrations (PM10) and traffic noise levels havebeen measured close to the highways Lundbyleden (close to HjalmarBrantingsplatsen) and E45 (on the Stena Denmark’s terminal) in central Gothenburg.Two things have been studied. First, the effects a noise barrier next to the highwayhave on the particle concentration and noise level around the highway. Second, howtwo different kinds of blocks can affect the concentration and levels on theircourtyards. Three samples of 15 minutes were taken at each measurement point. Todo this measurement a portable measurement station has been built. A particlesensor (DustTrak), a microphone and a GPS-receiver have been connected to asingle-board computer (Raspberry Pi). The data have been collected and processed inthe single-board computer.

    Only three repeated measurements were performed at each place of measurement,so the result in this study should be seen as an indicator of how particle and noisedistributions might look.

    In this study a noise barrier lowers the particle concentration by 50 % directly behindthe barrier and has a lowering effect up to 40 meters from the barrier when the windcomes from the road. The barrier lowers the noise levels directly behind the barrierby 16 dBA for a new glass and concrete barrier and by 12 dBA for an old woodenbarrier. The noise level is lowered for more than 100 meters from the barrier.

    In this study an old completely surrounded courtyard is better protected, against bothparticles and noise, than a new noise protected courtyard with several openings.Concerning particles no difference could be seen between inside and outside of thenew noise protected courtyard. The old completely surrounded courtyard had,however, 20 % lower particle concentrations than on the outside, assuming typicalbackground and traffic emissions. Concerning noise levels, both courtyards loweredthe levels by 6-7 dBA, compared to outside of the courtyard. The new noiseprotected courtyard lowered the levels less close to the openings.

  • 91.
    Granovskiy, Boris
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Gold, Jason M.
    Sumpter, David J. T.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Goldstone, Robert L.
    Integration of Social Information by Human Groups2015Inngår i: Topics in Cognitive Science, ISSN 1756-8757, E-ISSN 1756-8765, Vol. 7, nr 3, s. 469-493Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a situation in which individuals search for accurate decisions without direct feedback on their accuracy, but with information about the decisions made by peers in their group. The wisdom of crowds hypothesis states that the average judgment of many individuals can give a good estimate of, for example, the outcomes of sporting events and the answers to trivia questions. Two conditions for the application of wisdom of crowds are that estimates should be independent and unbiased. Here, we study how individuals integrate social information when answering trivia questions with answers that range between 0% and 100% (e.g., What percentage of Americans are left-handed?). We find that, consistent with the wisdom of crowds hypothesis, average performance improves with group size. However, individuals show a consistent bias to produce estimates that are insufficiently extreme. We find that social information provides significant, albeit small, improvement to group performance. Outliers with answers far from the correct answer move toward the position of the group mean. Given that these outliers also tend to be nearer to 50% than do the answers of other group members, this move creates group polarization away from 50%. By looking at individual performance over different questions we find that some people are more likely to be affected by social influence than others. There is also evidence that people differ in their competence in answering questions, but lack of competence is not significantly correlated with willingness to change guesses. We develop a mathematical model based on these results that postulates a cognitive process in which people first decide whether to take into account peer guesses, and if so, to move in the direction of these guesses. The size of the move is proportional to the distance between their own guess and the average guess of the group. This model closely approximates the distribution of guess movements and shows how outlying incorrect opinions can be systematically removed from a group resulting, in some situations, in improved group performance. However, improvement is only predicted for cases in which the initial guesses of individuals in the group are biased.

  • 92.
    Gustafsson, William
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Volatility modelling with exogenous binary variables2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 93.
    Gut, Allan
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Martin-Lof, Anders
    Extreme-trimmed St. Petersburg games2015Inngår i: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 96, s. 341-345Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let S-n, n >= 1, describe the successive sums of the payoffs in the classical St. Petersburg game. Feller's famous weak law, Feller (1945), states that s(n)/n log(2) n (sic) 1 as n -> infinity. However, almost sure convergence fails, more precisely, lim supn ->infinity S-n/n log(2) n = +infinity a.s. and lim inf(n ->infinity) S-n/n log(2) n = 1 a.s. as n -> infinity. Csorgo and Simons (1996) have shown that almost sure convergence holds for trimmed sums, that is, for S-n - max(1 <= k <= n) X-k and, moreover, that this remains true if the sums are trimmed by an arbitrary fixed number of maximal sums. A predecessor of the present paper was devoted to sums trimmed by the random number of maximal summands. The present paper concerns analogs for the random number of summands equal to the minimum, as well as analogs for joint trimmings. (C) 2014 Elsevier B.V. All rights reserved.

  • 94.
    Gut, Allan
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Martin-Löf, Anders
    Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden..
    A Maxtrimmed St. Petersburg Game2016Inngår i: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 29, nr 1, s. 277-291Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let S-n, n >= 1, describe the successive sums of the payoffs in the classical St. Petersburg game. The celebrated Feller weak law states that s(n)/n log(2)n ->(p) 1 as n -> infinity It is also known that almost sure convergence fails. However, Csorgo and Simons (Stat Probab Lett 26: 65-73, 1996) have shown that almost sure convergence holds for trimmed sums, that is, for S-n - max(1 <= k <= n) X-k. Since our actual distribution is discrete there may be ties. Our main focus in this paper is on the "maxtrimmed sum", that is, the sum trimmed by the random number of observations that are equal to the largest one. We prove an analog of Martin-Lof's (J Appl Probab 22: 634-643, 1985) distributional limit theorem for maxtrimmed sums, but also for the simply trimmed ones, as well as for the "total maximum". In a final section, we interpret these findings in terms of sums of (truncated) Poisson random variables.

  • 95.
    Gut, Allan
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Martin-Löf, Anders
    Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden.
    An Asymmetric St. Petersburg Game With Trimming2018Inngår i: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 50, nr A, s. 115-129Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let S-n, n >= 1, be the successive sums of the payoffs in the classical St. Petersburg game. The celebrated Feller weak law states that S-n/(n log(2) n) ->(P) 1 as n ->infinity. In this paper we review some earlier results of ours and extend some of them as we consider an asymmetric St. Petersburg game, in which the distribution of the payoff X is given by P(X = sr(k-1)) = pq(k-1), k = 1, 2,..., where p + q = 1 and s, r > 0. Two main results are extensions of the Feller weak law and the convergence in distribution theorem of Martin-Lof (1985). Moreover, it is well known that almost-sure convergence fails, though Csorgo and Simons (1996) showed that almost-sure convergence holds for trimmed sums and also for sums trimmed by an arbitrary fixed number of maxima. In view of the discreteness of the distribution we focus on 'max-trimmed sums', that is, on the sums trimmed by the random number of observations that are equal to the largest one, and prove limit theorems for simply trimmed sums, for max-trimmed sums, as well as for the 'total maximum'. Analogues with respect to the random number of summands equal to the minimum are also obtained and, finally, for joint trimming.

  • 96.
    Gut, Allan
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Stadtmueller, Ulrich
    Ulm Univ, Germany.
    A pointwise limit theorem for counting processes of perturbed random walks with an application to repeated significance tests2017Inngår i: Sequential Analysis, ISSN 0747-4946, E-ISSN 1532-4176, Vol. 36, nr 2, s. 290-298Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Hsu and Robbins (1947) introduced the concept of complete conver-gence as a complement to the Kolmogorov strong law in that they proved that Sigma(infinity)(n=1) P(|Sn| > n epsilon) < infinity provided the mean of the summands is zero and that the variance is finite. Later, Erdos proved the necessity (1949, 1950). Heyde (1975) proved that, under the same conditions, lim(epsilon)SE arrow 0 epsilon(2) Sigma(infinity)(n=1) P(|Sn| > n epsilon) = EX2, thereby opening an area of research that has been called precise asymptotics. Both results above have been extended and generalized in various directions. Kao (1978) proved a pointwise version of Heyde's result, viz. for the counting process N(epsilon) = Sigma(infinity)(n=1) 1{|Sn| > n epsilon}, he showed that lim(epsilon)SE arrow 0 epsilon N-2 (epsilon) ->(d) EX2 integral(infinity)(0) 1 {|W(u)| > u} du, where W(.) is the standard Wiener process. In this article, we prove an analog for perturbed random walks and illustrate how they enter naturally within the theory of repeated significance tests in exponential families.

  • 97.
    Gut, Allan
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Stadtmueller, Ulrich
    Univ Ulm, Dept Number Theory & Probabil Theory, D-89069 Ulm, Germany..
    Limit theorems for counting variables based on records and extremes2017Inngår i: Extremes, ISSN 1386-1999, E-ISSN 1572-915X, Vol. 20, nr 1, s. 33-52Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Hsu and Robbins (Proc. Nat. Acad. Sci. USA 33, 25-31, 1947) introduced the concept of complete convergence as a complement to the Kolmogorov strong law, in that they proved that provided the mean of the summands is zero and that the variance is finite. Later, ErdoIis proved the necessity. Heyde (J. Appl. Probab. 12, 173-175, 1975) proved that, under the same conditions, , thereby opening an area of research which has been called precise asymptotics. Both results above have been extended and generalized in various directions. Some time ago, Kao proved a pointwise version of Heyde's result, viz., for the counting process , he showed that , where W(ai...) is the standard Wiener process. In this paper we prove analogs for extremes and records for i.i.d. random variables with a continuous distribution function.

  • 98.
    Gut, Allan
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Stadtmueller, Ulrich
    Univ Ulm, Dept Number Theory & Probabil Theory, D-89069 Ulm, Germany..
    Strong laws for sequences in the vicinity of the LIL2017Inngår i: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 122, s. 63-72Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The present paper is devoted to strong laws of large numbers under moment conditions near those of the law of the iterated logarithm (LIL) for i.i.d sequences. More precisely, we wish to investigate possible limit theorems under moment conditions which are stronger than p for any p < 2, in which case we know that there is a.s. convergence to 0, and weaker than E X-2 < infinity, in which case the LIL holds.

  • 99.
    Gut, Allan
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Stadtmüller, Ulrich
    Ulm Univ, Dept Number Theory & Probabil Theory, D-89069 Ulm, Germany..
    Complete convergence for arrays and the law of the single logarithm2017Inngår i: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 96, nr 2, s. 333-344Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The present paper is devoted to complete convergence and the strong law of large numbers under moment conditions near those of the law of the single logarithm (LSL) for independent and identically distributed arrays. More precisely, we investigate limit theorems under moment conditions which are stronger than 2p for any p < 2, in which case we know that there is almost sure convergence to 0, and weaker than E X-4 = (log(+) vertical bar X vertical bar)(2) < infinity, in which case the LSL holds.

  • 100.
    Gyllingberg, Linnéa
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Mean field approximations of spatial models of evolution2016Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
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