Logo: to the web site of Uppsala University

uu.sePublications from Uppsala University
Change search
Refine search result
1 - 32 of 32
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1.
    Bandyopadhyay, Antar
    et al.
    Indian Stat Inst, Delhi, India.;Indian Stat Inst, Kolkata, India.;Indian Stat Inst, Theoret Stat & Math Unit, Delhi Ctr, 7 SJS Sansanwal Marg, New Delhi 110016, India..
    Janson, Svante
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Thacker, Debleena
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Strong convergence of infinite color balanced urns under uniform ergodicity2020In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 57, no 3, p. 853-865, article id PII S0021900220000376Article in journal (Refereed)
    Abstract [en]

    We consider the generalization of the Polya urn scheme with possibly infinitely many colors, as introduced in [37], [4], [5], and [6]. For countably many colors, we prove almost sure convergence of the urn configuration under theuniform ergodicityassumption on the associated Markov chain. The proof uses a stochastic coupling of the sequence of chosen colors with abranching Markov chainon a weightedrandom recursive treeas described in [6], [31], and [26]. Using this coupling we estimate the covariance between any two selected colors. In particular, we re-prove the limit theorem for the classical urn models with finitely many colors.

  • 2.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology.
    Bartoszek, Wojciech
    Gdansk University of Technology.
    On the Time Behaviour of Okazaki Fragments2006In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 43, p. 500-509Article in journal (Refereed)
    Abstract [en]

    We find explicit analytical formulae for the time dependence of the probability of the number of Okazaki fragments produced during the process of DNA replication. This extends a result of Cowan on the asymptotic probability distribution of these fragments.

  • 3.
    Bartoszek, Krzysztof
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sagitov, Serik
    Chalmers University of Technology and the Unversity of Gothenburg.
    Phylogenetic confidence intervals for the optimal trait value2015In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, no 4, p. 1115-1132Article in journal (Refereed)
    Abstract [en]

    We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree ismodelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein–Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the samplemean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean isapproximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.

  • 4.
    Bayraktar, Erhan
    et al.
    Univ Michigan, Dept Math, 530 Church St, Ann Arbor, MI 48104 USA.
    Ekström, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Probability Theory and Combinatorics.
    Guo, Jia
    Univ Michigan, Dept Math, 530 Church St, Ann Arbor, MI 48104 USA.
    Disorder detection with costly observations2022In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 59, no 2, p. 338-349, article id PII S0021900221000632Article in journal (Refereed)
    Abstract [en]

    We study the Wiener disorder detection problem where each observation is associated with a positive cost. In this setting, a strategy is a pair consisting of a sequence of observation times and a stopping time corresponding to the declaration of disorder. We characterize the minimal cost of the disorder problem with costly observations as the unique fixed point of a certain jump operator, and we determine the optimal strategy.

  • 5.
    Björnberg, Jakob E.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Britton, T.
    Broman, E. I.
    Natan, E.
    A Stochastic Model for Virus Growth in a Cell Population2014In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 51, no 3, p. 599-612Article in journal (Refereed)
    Abstract [en]

    In this work we introduce a stochastic model for the spread of a virus in a cell population where the virus has two ways of spreading: either by allowing its host cell to live and duplicate, or by multiplying in large numbers within the host cell, causing the host cell to burst and thereby let the virus enter new uninfected cells. The model is a kind of interacting Markov branching process. We focus in particular on the probability that the virus population survives and how this depends on a certain parameter A which quantifies the 'aggressiveness' of the virus. Our main goal is to determine the optimal balance between aggressive growth and long-term success. Our analysis shows that the optimal strategy of the virus (in terms of survival) is obtained when the virus has no effect on the host cell's life cycle, corresponding to lambda = 0. This is in agreement with experimental data about real viruses.

  • 6.
    Björnberg, Jakob E.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Broman, Erik I.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Coexistence and noncoexistence of Markovian viruses and their hosts2014In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 51, no 1, p. 191-208Article in journal (Refereed)
    Abstract [en]

    Examining possibilities for the coexistence of two competing populations is a classic problem which dates back to the earliest 'predator-prey' models. In this paper we study this problem in the context of a model introduced in Bjornberg et al. (2012) for the spread of a virus infection in a population of healthy cells. The infected cells may be seen as a population of 'predators' and the healthy cells as a population of 'prey'. We show that, depending on the parameters defining the model, there may or may not be coexistence of the two populations, and we give precise criteria for this.

  • 7. Britton, Tom
    et al.
    Lindholm, Mathias
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    Turova, Tatyana
    A dynamic network in a dynamic population: Asymptotic properties2011In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 48, no 4, p. 1163-1178Article in journal (Refereed)
    Abstract [en]

    We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the life of a node it creates edges to other nodes, nodes with high social index at higher rate, and edges disappear randomly in time. For this model, we derive a criterion for when a giant connected component exists after the process has evolved for a long period of time, assuming that the node population grows to infinity. We also obtain an explicit expression for the degree correlation rho (of neighbouring nodes) which shows that rho is always positive irrespective of parameter values in one of the two treated submodels, and may be either positive or negative in the other model, depending on the parameters.

  • 8.
    Ekström, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Bounds for perpetual American option prices in a jump-diffusion model2006In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 43, no 3, p. 867-873Article in journal (Refereed)
  • 9.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Glover, Kristoffer
    Univ Technol Sydney, POB 123, Broadway, NSW 2007, Australia..
    Leniec, Marta
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Dynkin Games With Heterogeneous Beliefs2017In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 54, no 1, p. 236-251Article in journal (Refereed)
    Abstract [en]

    We study zero-sum optimal stopping games (Dynkin games) between two players who disagree about the underlying model. In a Markovian setting, a verification result is established showing that if a pair of functions can be found that satisfies some natural conditions, then a Nash equilibrium of stopping times is obtained, with the given functions as the corresponding value functions. In general, however, there is no uniqueness of Nash equilibria, and different equilibria give rise to different value functions. As an example, we provide a thorough study of the game version of the American call option under heterogeneous beliefs. Finally, we also study equilibria in randomized stopping times.

  • 10.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Janson, Svante
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Tysk, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Superreplication of options on several underlying assets2005In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 42, no 1, p. 27-38Article in journal (Refereed)
  • 11.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Lindberg, Carl
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Optimal closing of a momentum trade2013In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 50, no 2, p. 374-387Article in journal (Refereed)
    Abstract [en]

    There is an extensive academic literature that documents that stocks which have performed well in the past often continue to perform well over some holding period-so-called momentum. We study the optimal timing for an asset sale for an agent with a long position in a momentum trade. The asset price is modelled as a geometric Brownian motion with a drift that initially exceeds the discount rate, but with the opposite relation after an unobservable and exponentially distributed time. The problem of optimal selling of the asset is then formulated as an optimal stopping problem under incomplete information. Based on the observations of the asset, the agent wants to detect the unobservable change point as accurately as possible. Using filtering techniques and stochastic analysis, we reduce the problem to a one-dimensional optimal stopping problem, which we solve explicitly. We also show that the optimal boundary at which the investor should liquidate the trade depends monotonically on the model parameters.

  • 12.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Lindberg, Carl
    Tysk, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Wanntorp, Henrik
    Optimal liquidation of a call spread2010In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 47, no 2, p. 586-593Article in journal (Refereed)
    Abstract [en]

    We study the optimal liquidation strategy for a call spread in the case when an investor, who does not hedge, believes in a volatility that differs from the implied volatility. The liquidation problem is formulated as an optimal stopping problem, which we solve explicitly. We also provide a sensitivity analysis with respect to the model parameters.

  • 13.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Olofsson, Marcus
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Vannestål, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    A renewal theory approach to two-state switching problems with infinite values2020In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 57, no 1, p. 1-18Article in journal (Refereed)
    Abstract [en]

    We study a renewal theory approach to perpetual two-state switching problems with infinite value functions. Since the corresponding value functions are infinite, the problems fall outside the standard class of problems which can be analyzed using dynamic programming. Instead, we propose an alternative formulation of optimal switching theory in which optimality of a strategy is defined in terms of its long-term mean return, which can be determined using renewal theory. The approach is illustrated by examples in connection with trend-following strategies in finance.

  • 14.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Vannestål, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Momentum liquidation under partial information2016In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 2, p. 341-359Article in journal (Refereed)
    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.

  • 15.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Probability Theory and Combinatorics.
    Wang, Yuqiong
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Probability Theory and Combinatorics.
    Stopping problems with an unknown state2023In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072Article in journal (Refereed)
  • 16.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Wanntorp, Henrik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Optimal stopping of a Brownian bridge2009In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 46, no 1, p. 170-180Article in journal (Refereed)
    Abstract [en]

     We study several optimal stopping problems in which the gains process is a Brownian bridge or a functional of a Brownian bridge. Our examples constitute natural finite-horizon optimal stopping problems with explicit solutions.

  • 17.
    Gabrysch, Katja
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Convergence of directed random graphs to the Poisson-weighted infinite tree2016In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 2, p. 463-474Article in journal (Refereed)
    Abstract [en]

    We consider a directed graph on the integers with a directed edge from vertex i to j present with probability n-1, whenever i<j, independently of all other edges. Moreover, to each edge (i,j) we assign weight n-1(j - i). We show that the closure of vertex 0 in such a weighted random graph converges in distribution to the Poisson-weighted infinite tree as n→∞. In addition, we derive limit theorems for the length of the longest path in the subgraph of the Poisson-weighted infinite tree which has all vertices at weighted distance of at most ρ from the root.

  • 18.
    Gabrysch, Katja
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Distribution of the smallest visited point in a greedy walk on the line2016In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 3, p. 880-887Article in journal (Refereed)
    Abstract [en]

    We consider a greedy walk on a Poisson process on the real line. It is known that the walk does not visit all points of the process. In this paper we first obtain some useful independence properties associated with this process which enable us to compute the distribution of the sequence of indices of visited points. Given that the walk tends to +∞, we find the distribution of the number of visited points in the negative half-line, as well as the distribution of the time at which the walk achieves its minimum.

  • 19.
    Gut, Allan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    Limit theorems for a generalized St Petersburg game2010In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 47, no 3, p. 752-760Article in journal (Refereed)
    Abstract [en]

    The topic of the present paper is a generalized St Petersburg game in which the distribution of the payoff X is given by P(X = sr((k-1)/alpha)) = pq(k-1), k = 1,2, ..., where p + q = 1, s = l/p, r = 1/q, and 0 < alpha <= 1. For the case in which alpha = 1, we extend Feller's classical weak law and Martin-Lof's theorem on convergence in distribution along the 2"-subsequence. The analog for 0 < alpha < 1 turns out to converge in distribution to an asymmetric stable law with index a. Finally, some limit theorems for polynomial and geometric size total gains, as well as for extremes, are given.

  • 20.
    Gut, Allan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Stadtmüller, Ulrich
    Ulm Univ, Dept Number & Probabil Theory, D-89069 Ulm, Germany..
    Variations of the elephant random walk2021In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 58, no 3, p. 805-829Article in journal (Refereed)
    Abstract [en]

    In the classical simple random walk the steps are independent, that is, the walker has no memory. In contrast, in the elephant random walk, which was introduced by Schutz and Trimper [19] in 2004, the next step always depends on the whole path so far. Our main aim is to prove analogous results when the elephant has only a restricted memory, for example remembering only the most remote step(s), the most recent step(s), or both. We also extend the models to cover more general step sizes.

  • 21.
    Holst, Lars
    et al.
    Royal Inst Technol, Dept Math, SE-10044 Stockholm, Sweden..
    Konstantopoulos, Takis
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Runs In Coin Tossing: A General Approach For Deriving Distributions For Functionals2015In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, no 3, p. 752-770Article in journal (Refereed)
    Abstract [en]

    We take a fresh look at the classical problem of runs in a sequence of independent and identically distributed coin tosses and derive a general identity/recursion which can be used to compute (joint) distributions of functionals of run types. This generalizes and unifies already existing approaches. We give several examples, derive asymptotics, and pose some further questions.

  • 22.
    Janson, Svante
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    ON DEGENERATE SUMS OF m-DEPENDENT VARIABLES2015In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, no 4, p. 1146-1155Article in journal (Refereed)
    Abstract [en]

    It is well known that the central limit theorem holds for partial sums of a stationary sequence (X-i) of m-dependent random variables with finite variance; however, the limit may be degenerate with variance 0 even if var(X-i) not equal 0. We show that this happens only in the case when X-i - EXi = Y-i - Y-i for an (m - 1)-dependent stationary sequence (Y-i) with finite variance (a result implicit in earlier results), and give a version for block factors. This yields a simple criterion that is a sufficient condition for the limit not to be degenerate. Two applications to subtree counts in random trees are given.

  • 23.
    Janson, Svante
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Rate of convergence for traditional Polya urns2020In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 57, no 4, p. 1029-1044, article id PII S0021900220000595Article in journal (Refereed)
    Abstract [en]

    Consider a Polya urn with balls of several colours, where balls are drawn sequentially and each drawn ball is immediately replaced together with a fixed number of balls of the same colour. It is well known that the proportions of balls of the different colours converge in distribution to a Dirichlet distribution. We show that the rate of convergence is Theta(1/n) in the minimal L-p metric for any p is an element of [1,infinity], extending a result by Goldstein and Reinert; we further show the same rate for the Levy distance, while the rate for the Kolmogorov distance depends on the parameters, i.e. on the initial composition of the urn. The method used here differs from the one used by Goldstein and Reinert, and uses direct calculations based on the known exact distributions.

  • 24.
    Janson, Svante
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    The probability that a rqandom multigraph is simple II2014In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 51A, p. 123-137Article in journal (Refereed)
  • 25.
    Janson, Svante
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Linusson, Svante
    The probability of the Alabama paradox2012In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 49, no 3, p. 773-794Article in journal (Refereed)
    Abstract [en]

    Hamilton's method is a natural and common method to distribute seats proportionally between states (or parties) in a parliament. In the USA it has been abandoned due to some drawbacks, in particular the possibility of the Alabama paradox, but it is still in use in many other countries. In this paper we give, under certain assumptions, a closed formula for the asymptotic probability, as the number of seats tends to infinity, that the Alabama paradox occurs given the vector p(l), ..., p(m) of relative sizes of the states. From the formula we deduce a number of consequences. For example, the expected number of states that will suffer from the Alabama paradox is asymptotically bounded above by 1/e and on average approximately 0.123.

  • 26.
    Janson, Svante
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Luczak, Tomasz
    Norros, Ilkka
    Large cliques in a power-law random graph2010In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 47, no 4, p. 1124-1135Article in journal (Refereed)
    Abstract [en]

    In this paper we study the size of the largest clique omega(G(n, alpha)) in a random graph G(n, alpha) on n vertices which has power-law degree distribution with exponent alpha. We show that, for 'flat' degree sequences with alpha > 2, with high probability, the largest clique in G(n, alpha) is of a constant size, while, for the heavy tail distribution, when 0 < alpha < 2, omega(G (n, alpha)) grows as a power of n. Moreover, we show that a natural simple algorithm with high probability finds in G(n, alpha) a large clique of size (1 - o(1))omega(G(n, alpha)) in polynomial time.

  • 27. Janson, Svante
    et al.
    Petersson, Niclas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    The integral of the supremum process of Brownian motion2009In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 46, no 2, p. 593-600Article in journal (Refereed)
    Abstract [en]

    In this paper we study the integral of the supremum process of standard   Brownian motion. We present an explicit formula for the moments of the   integral (or area) A(T) covered by the process in the time interval [0,   T]. The Laplace transform of A(T) follows as a consequence. The main   proof involves a double Laplace transform of A(T) and is based on   excursion theory and local time for Brownian motion.

  • 28.
    Konstantopoulos, Takis
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Liu, Zhenxia
    Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden..
    Yang, Xiangfeng
    Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden..
    Laplace Transform Asymptotics and Large Deviation Principles for Longest Success Runs in Bernoulli Trials2016In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 3, p. 747-764Article in journal (Refereed)
    Abstract [en]

    The longest stretch L(n) of consecutive heads in n independent and identically distributed coin tosses is seen from the prism of large deviations. We first establish precise asymptotics for the moment generating function of L(n) and then show that there are precisely two large deviation principles, one concerning the behavior of the distribution of L(n) near its nominal value log(1/p) n and one away from it. We discuss applications to inference and to logarithmic asymptotics of functionals of L(n).

  • 29.
    Konstantopoulos, Takis
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Yuan, Linglong
    Xian Jiaotong Liverpool Univ, Dept Math Sci, 111 Renai Rd, Suzhou 215123, Peoples R China..
    A PROBABILISTIC INTERPRETATION OF THE GAUSSIAN BINOMIAL COEFFICIENTS2017In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 54, no 4, p. 1295-1298Article in journal (Refereed)
    Abstract [en]

    We present a stand-alone simple proof of a probabilistic interpretation of the Gaussian binomial coefficients by conditioning a random walk to hit a given lattice point at a given time.

  • 30.
    Lu, Bing
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Recovering a piecewise constant volatility from perpetual put option prices2010In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 47, no 3, p. 680-692Article in journal (Refereed)
    Abstract [en]

    In this paper we present a method to recover a time-homogeneous piecewise constant volatility from a finite set of perpetual put option prices. The whole calculation process of the volatility is decomposed into easy computations in many fixed disjoint intervals. In each interval, the volatility is obtained by solving a system of nonlinear equations.

  • 31.
    Meiners, Matthias
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    An almost-sure renewal theorem for branching random walks on the line2010In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 47, no 3, p. 811-825Article in journal (Refereed)
    Abstract [en]

    In the present paper an almost-sure renewal theorem for branching random walks (BRWs) on the real line is formulated and established. The theorem constitutes a generalization of Nerman's theorem on the almost-sure convergence of Malthus normed supercritical Crump-Mode-Jagers branching processes counted with general characteristic and Gatouras' almost-sure renewal theorem for BRWs on a lattice.

  • 32.
    Thörnblad, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    The dominating colour of an infinite Pólya urn model2016In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 3, p. 914-924Article in journal (Refereed)
    Abstract [en]

    We study a Pólya-type urn model defined as follows. Start at time 0 with a single ball of some colour. Then, at each time n≥1, choose a ball from the urn uniformly at random. With probability ½<p<1, return the ball to the urn along with another ball of the same colour. With probability 1−p, recolour the ball to a new colour and then return it to the urn. This is equivalent to the supercritical case of a random graph model studied by Backhausz and Móri (2015), (2016) and Thörnblad (2015). We prove that, with probability 1, there is a dominating colour, in the sense that, after some random but finite time, there is a colour that always has the most number of balls. A crucial part of the proof is the analysis of an urn model with two colours, in which the observed ball is returned to the urn along with another ball of the same colour with probability p, and removed with probability 1−p. Our results here generalise a classical result about the Pólya urn model (which corresponds to p=1).

1 - 32 of 32
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf