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Klimek, Maciej
Publications (10 of 40) Show all publications
Alghamdi, A. & Klimek, M. (2017). Probabilistic approximation of partly filled-in composite Julia sets. Annales Polonici Mathematici, 119(3), 203-220
Open this publication in new window or tab >>Probabilistic approximation of partly filled-in composite Julia sets
2017 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 119, no 3, p. 203-220Article in journal (Refereed) Published
Abstract [en]

We study properties of the metric space of pluriregular sets and of contractions on that space induced by finite families of proper polynomial mappings of several complex variables. In particular, we show that closed balls in the space of pluriregular sets do not have to be compact and we give a simple proof of applicability of the so-called chaos game in the case of composite Julia sets. Part of the construction of those sets also leads to a computationally viable approximation by simpler sets based on Monte-Carlo simulation.

Keyword
composite Julia sets, pluricomplex Green functions, iterated function system, the chaos game, complex dynamics, Monte-Carlo simulation
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-339527 (URN)10.4064/ap4100-8-2017 (DOI)000417986400002 ()
Available from: 2018-01-22 Created: 2018-01-22 Last updated: 2018-01-22Bibliographically approved
Klimek, M. (2015). Stochastic characterization of plurisubharmonicity and convexity of functions. In: Leokadia Bialas-Ciez and Marta Kosek (Ed.), Constructive Approximation of Functions: (pp. 175-181). Warszawa: Institute of Mathematics, Polish Academy of Sciences
Open this publication in new window or tab >>Stochastic characterization of plurisubharmonicity and convexity of functions
2015 (English)In: Constructive Approximation of Functions / [ed] Leokadia Bialas-Ciez and Marta Kosek, Warszawa: Institute of Mathematics, Polish Academy of Sciences , 2015, p. 175-181Chapter in book (Refereed)
Abstract [en]

It is shown that both plurisubharmonicity and convexity of functions can be characterized in terms of Brownian motions with individually scaled components. Applications related to multivariable Jensen's inequality are also given.

Place, publisher, year, edition, pages
Warszawa: Institute of Mathematics, Polish Academy of Sciences, 2015
Series
Banach Center Publications, ISSN 0137-6934 ; Vol. 107
Keyword
plurisubharmonic functions, convex functions, Brownian motion
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-206703 (URN)978-83-86806-30-0 (ISBN)
Available from: 2013-09-03 Created: 2013-09-03 Last updated: 2016-05-12
Klimek, M. (2011). The price of a rose: How names influence pricing?. Charaktery - Magazyn Psychologiczny, May, 100-103
Open this publication in new window or tab >>The price of a rose: How names influence pricing?
2011 (Polish)In: Charaktery - Magazyn Psychologiczny, ISSN 1427-695X, Vol. May, p. 100-103Article, review/survey (Other (popular science, discussion, etc.)) Published
National Category
Mathematics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
urn:nbn:se:uu:diva-293136 (URN)
Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-12
Klimek, M. (2010). Reckoning with probability. Charaktery - Magazyn Psychologiczny, September, 76-79
Open this publication in new window or tab >>Reckoning with probability
2010 (Polish)In: Charaktery - Magazyn Psychologiczny, ISSN 1427-695X, Vol. September, p. 76-79Article, review/survey (Other (popular science, discussion, etc.)) Published
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-293135 (URN)
Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-12
Klimek, M. (2010). Tracking the invisible science: Why does mathematics stay in the shadow of other sciences?. Charaktery - Magazyn Psychologiczny, May, 80-82
Open this publication in new window or tab >>Tracking the invisible science: Why does mathematics stay in the shadow of other sciences?
2010 (Polish)In: Charaktery - Magazyn Psychologiczny, ISSN 1427-695X, Vol. May, p. 80-82Article, review/survey (Other (popular science, discussion, etc.)) Published
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-293134 (URN)
Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-12
Klimek, M. & Kosek, M. (2009). Generalized iterated function systems, multifunctions and Cantor sets. Annales Polonici Mathematici, 96(1), 25-41
Open this publication in new window or tab >>Generalized iterated function systems, multifunctions and Cantor sets
2009 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 96, no 1, p. 25-41Article in journal (Refereed) Published
Abstract [en]

Using a construction similar to an iterated function system, but withfunctions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.

Place, publisher, year, edition, pages
Warsaw: IM PAN, 2009
Keyword
holomorphic mappings, analytic multifunctions, set-valued functions, affine contractions, iterations, generalized Cantor sets
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-104373 (URN)10.4064/ap96-1-2 (DOI)000271321900002 ()
Available from: 2009-05-28 Created: 2009-05-28 Last updated: 2017-12-13
Klimek, M. (2008). Change of expected value under equivalent probability measures and use of surrogate assets.
Open this publication in new window or tab >>Change of expected value under equivalent probability measures and use of surrogate assets
2008 (English)Report (Other academic)
Publisher
p. 8
Series
U.U.D.M. report / Uppsala University, Department of Mathematics, ISSN 1101-3591 ; 2008:41
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-142978 (URN)
Available from: 2011-01-18 Created: 2011-01-18 Last updated: 2016-05-12
Klimek, M., Matsuura, M. & Okabe, Y. (2008). Stochastic flows and finite block frames. Journal of Mathematical Analysis and Applications, 342(2), 816-829
Open this publication in new window or tab >>Stochastic flows and finite block frames
2008 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 342, no 2, p. 816-829Article in journal (Refereed) Published
Abstract [en]

With the aim of understanding the mathematical structure of the fluctuation–dissipation theorem in non-equilibrium statistical physics and then constructing a mathematical principle in the modeling problem for time series analysis, we have developed the theory of KM2O-Langevin equations for discrete time stochastic processes. In this paper, as a new method for model analysis in the theory of KM2O-Langevin equations, we show that block frames provide a natural mathematical language for dealing with minimum norm expansions of multi-dimensional stochastic processes which do not necessarily satisfy stationarity and non-degeneracy conditions.

Keyword
degenerate flows, block frames, minimum norm solutions, fluctuation-dissipation theorem
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-87336 (URN)10.1016/j.jmaa.2007.12.015 (DOI)000254945300007 ()
Available from: 2008-09-16 Created: 2008-09-16 Last updated: 2017-12-13
Klimek, M. (2006). Degenerate non-stationary flows and finite block frames.
Open this publication in new window or tab >>Degenerate non-stationary flows and finite block frames
2006 (English)Report (Other academic)
Series
UUDM ; 2006:2
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-23853 (URN)
Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2016-05-12
Klimek, M. & Kosek, M. (2006). Strong Analyticity of Partly Filled-in Composite Julia Sets. Set-Valued Analysis, 14, 55-68
Open this publication in new window or tab >>Strong Analyticity of Partly Filled-in Composite Julia Sets
2006 (English)In: Set-Valued Analysis, Vol. 14, p. 55-68Article in journal (Refereed) Published
National Category
Other Mathematics
Identifiers
urn:nbn:se:uu:diva-21208 (URN)
Available from: 2006-12-15 Created: 2006-12-15 Last updated: 2016-05-11
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