Asymptotic methods in stochastics  Page description

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Details of project

 
Identifier
108615
Type K
Principal investigator Csáki, Endre
Title in Hungarian Aszimptotikus módszerek a sztochasztikában
Title in English Asymptotic methods in stochastics
Keywords in Hungarian határeloszlás tételek, invariancia, véletlen bolyongás, függő folyamatok, véletlen kombinatorikai struktúrák
Keywords in English limit theorems, invariance, random walk, dependent processes, random combinatorial structures
Discipline
Mathematics (Council of Physical Sciences)100 %
Ortelius classification: Probability theory
Panel Mathematics and Computing Science
Department or equivalent Alfréd Rényi Institute of Mathematics, HAS
Participants Backhausz, Ágnes Mariann
Berkes, István
Horváth, Lajos
Móri, Tamás
Révész, Pál
Starting date 2013-09-01
Closing date 2017-12-31
Funding (in million HUF) 7.405
FTE (full time equivalent) 8.84
state running project





 

Final report

 
Results in Hungarian
Időben fejlődő különféle véletlen kombinatorikai struktúrák (köztük véletlen gráfok) jellemzőinek aszimptotikus viselkedését vizsgáltuk. Gyenge és erős invarianciát bizonyítottunk az un. pók struktúrán való bolyongás magasságára, lokális és tartózkodási idejére. Bizonyos gráfokon történő 2 vagy több bolyongások közti távolságokra. Anizotropikus bolyongások néhány tulajdonságát vizsgáltuk. Számos határeloszlástételt bizonyítottunk az un. szentpétervári játékra, többek között egy erős invariancia elvet vonzási tartományba nem tartozó valószínűségi változókra. Kiterjesztettük a Komlós-Major-Tusnády approximációtételt függő folyamatokra. Pontos kritériumot adtunk általánosított Fourier sorok egy osztályának majdnem mindenütt való konvergenciájára. Aszimptotikus eredményeket bizonyítottunk gyengén függő valószínűségi változók megnyírt összegeire és kiterjesztettük az un. CUSUM módszert függő folyamatokban fellépő változások felismerésére. Bebizonyítottuk az un. "részsorozat elv" egy egyenletes formáját, funkcionálanalízisbeli alkalmazásokkal. Elméleti biológiai problémák által motivált matematikai modelleket építettünk és elemeztünk a sztochasztika, a játékelmélet és a differenciálegyenletek elméletének módszereivel. Folytattuk korábbi kutatásainkat a többdimenziós eloszlásokkal kapcsolatos valószínűségekre, ill. a diszkrét eloszlások eltérésére adott becslések területén.
Results in English
We investigated the asymptotic behavior of numerical characteristics of certain random combinatorial structures (including random graphs) evolving in time. We proved weak and strong invariance principles for heights, local and occupation times of random walks on spider. We proved some results for the distance between 2 or more random walks on certain graphs. The properties of certain anisotropic random walks were investigated. We proved several limit theorems for the St. Petersburg game and obtained a strong invariance principle for i.i.d. random variables not belonging to any domain of attraction. We extended the Komlós-Major-Tusnády strong approximation theorem to dependent random variables. We gave optimal convergence criteria for a class of generalized Fourier series. We proved asymptotic results for trimmed sums of weakly dependent random variables and extended the classical CUSUM change point method for dependent processes. We proved a uniform version of the so called "subsequence principle"with applications in functional analysis. We constructed and analysed mathematical models motivated by theoretical biology with method of stochastics, game theory, and the theory of differential equations. We continued our earlier research and gave new estimations for the probabilities ralated to multivariate probability measures and for the deviation of discrete probability distributions.
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=108615
Decision
Yes





 

List of publications

 
Garay J; Cressman R; Móri TF; Varga T:: The ESS and replicator equation in matrix games under time constraints, Journal of Mathematical Biology, to appear, 2018
Berkes I; Aistleitner C; Seip K: GCD sums from Poisson integrals and dilated sums, Journal of European Mathematical Society 17: 1517-1546, 2015
Berkes I; Tichy R: Lacunary series and stable distributions, In Mathematical Statistics and Limit Theorems: Festschrift in Honor of Paul Deheuvels, Springer, Berlin, 7-19, 2015
Berkes I; Raseta M: On the discrepancy and empirical distribution function of $\{n_k\alpha\}$, Uniform Distribution Theory 10: 1-17, 2015
Berkes I; Tichy R: On permutation-invariance of limit theorems, Journal of Complexity 31: 372-379, 2015
Csáki E; Csörgő M: On Bahadur-Kiefer type processes for sums and renewals in dependent cases, In Mathematical Statistics and Limit Theorems: Festschrift in Honor of Paul Deheuvels, Springer, Berlin, 93-103, 2015
Csáki E; Földes A; Révész P: Some results and problems for anisotropic random walk on the plane, Asymptotic Laws and Methods in Stochastics: Festschrift in Honor of Miklós Csörgő, Springer, Berlin, 55-75, 2015
Révész P: On the area of the largest square covered by a comb-random-walk, Asymptotic Laws and Methods in Stochastics: Festschrift in Honor of Miklós Csörgő, Springer, Berlin, 77-85, 2015
Backhausz Á; Móri TF: Further properties of a random graph with duplications and delations, Stochastic Models 32: 99-120, 2016
Berkes I; Tichy R: Lacunary series and stable distributions, In Mathematical Statistics and Limit Theorems: Festschrift in Honor of Paul Deheuvels, Springer, Berlin, 7-19, 2015
Csáki, E; Földes, A; Révész, P: About the distance between random walkers on some graphs, Periodica Mathematica Hungarica, to appear (accepted for publication), 2017
Bazarova, A; Berkes, I; Horváth, L: Change point detection with stable AR(1) errors, In: Asymptotic Laws and Methods in Stochastics, Festschrift in honor of Miklós Csörgő, Springer, Berlin, 179-193, 2015
Bazarova, A; Berkes, I; Horváth, L: On the extremal theory of continued fractions, Journal of Theoretical Probability 29: 248-266, 2016
Aistleitner, A; Berkes, I; Seip, K; Weber, M: Convergence of series of dilated functions and spectral norms of GCD matrices, Acta Arithmetica 168: 221-246, 2015
Berkes, I; Tichy, R: The Kadec-Pelczinski theorem in $L^p$, Proceedings of American Mathematical Society 144: 2053-2066, 2016
Csáki E; Csörgő M; Földes A; Révész P: Some limit theorems for heights of random walks on a spider, Journal of Theoretical Probability 29: 1685-1709, 2016
Csáki E; Csörgő M; Kulik R: Strong approximations for long memory sequences based partial sums, counting and their Vervaat processes, Periodica Mathematica Hungarica 73: 208-223, 2016
Csáki, E; Földes, A; Révész, P: About the distance between random walkers on some graphs, Periodica Mathematica Hungarica 75: 36-57, 2017
Berkes I: Strong approximation of the St. Petersburg game, Statistics 51: 3-10, 2017
Berkes I; Győrfi L; Kevei P: Tail probabilities of St. Petersburg sums, trimmed sums, and their limit, Journal of Theoretical Probability 30: 1104-1129, 2017
Csáki E; Csörgő M; Földes A; Révész P: Limit theorems for local and occupation times of random walks and Brownian motion on a spider, Journal of Theoretical Probability, submitted, revised according to referee remarks; arXiv:1609.08710v2 [math.PR], 2018
Garay V; Csiszár V; Móri TF: Evolutionary stability for matrix games under time constraints, Journal of Theoretical Biology 415: 1-12, 2017
Garay V; Csiszár V; Móri TF: Survival phenotype, selfish individual versus Darwinian phenotype, Journal of Theoretical Biology 430: 86-91, 2017
Móri TF: Accuracy of approximation for discrete distributions, Journal of Probability and Statistics, Article ID 6212567, 2016
Móri TF; Székely G: Representations by uncorrelated random variables, Mathematical Methods of Statistics 26: 149-153, 2017
Móri TF; Rokob S: A random graph model driven by time-dependent branching dynamics, Annales Univ. Sci. Budapest. Sect. Comp. 46, in print, 2017
Berkes I; Fukuyama K; Nishimura T: A metric discrepancy result with given speed, Acta Mathematica Hungarica 151: 199-216, 2017
Backhausz Á; Kunszenti-Kovács D: On the dense preferential attachment graph models and their graphon induced counterpart, Journal of Applied Probability, submitted; arXiv:1701.06760v1 [math.CO]; decision expected in October, 2018
Móri TF; Rokob S: A random graph model driven by time-dependent branching dynamics, Annales Univ. Sci. Budapest. Sect. Comp. 46: 191-213, 2017
Backhausz Á; Kunszenti-Kovács D: On the dense preferential attachment graph models and their graphon induced counterpart, Journal of Applied Probability, submitted; arXiv:1701.06760v1 [math.CO];, 2018
Csáki E; Csörgő M; Földes A; Révész P: Limit theorems for local and occupation times of random walks and Brownian motion on a spider, Journal of Theoretical Probability, to appear; arXiv: 1609.08710v2 [math.PR], 2018
Berkes I; Liu W; Wu WB: Komlós-Major-Tusnády approximation under dependence, Annals of Probability 42: 794-817, 2014
Bazarova A; Berkes I; Horváth L: On the central limit theorem for modulus trimmed sum, Statistics and Probability Letters 86: 61-67, 2014
Bazarova A; Berkes I; Horváth L: Trimmed stable autoregressive processes, Stochastic Processes and Applications 124: 3441-3462, 2014
Csáki E; Csörgő M: On Bahadur-Kiefer type processes for sums and renewals in dependent cases, In Mathematical Statistics and Limit Theorems: Festschrift in Honor of Paul Deheuvels, Springer, Berlin, to appear (accepted for publication), 2015
Csáki E; Földes A; Révész P: Some results and problems for anisotropic random walk on the plane, Asymptotic Laws and Methods in Stochastics: Festschrift in Honor of Miklós Csörgő, Springer, Berlin, to appear (accepted for publication), 2014
Révész P: On the area of the largest square covered by a comb-random-walk, Asymptotic Laws and Methods in Stochastics: Festschrift in Honor of Miklós Csörgő, Springer, Berlin, to appear (accepted for publication), 2014
Csiszár V; Fegyverneki T; Móri TF: Explicit multivariate bounds of Chebyshev type, Annales Univ. Sci. Budapest, Sect. Comp. 42 (accepted for publication), 2014
Backhausz Á; Móri TF: A random model of publication activity, Discrete Applied Mathematics 162: 78-89, 2014
Backhausz Á; Móri TF: Asymptotics of a renewal-like recursion and an integral equation, Applicable Analysis and Discrete Mathematics 8 (accepted for publication), 2014
Backhausz Á; Móri TF: Asymptotic properties of a random graph with duplications, Journal of Applied Probability (accepted for publication), 2014
Csáki E; Csörgő M: On Bahadur-Kiefer type processes for sums and renewals in dependent cases, In Mathematical Statistics and Limit Theorems: Festschrift in Honor of Paul Deheuvels, Springer, Berlin, 93-103, 2015
Csáki E; Földes A; Révész P: Some results and problems for anisotropic random walk on the plane, Asymptotic Laws and Methods in Stochastics: Festschrift in Honor of Miklós Csörgő, Springer, Berlin, to appear (accepted for publication), 2015
Révész P: On the area of the largest square covered by a comb-random-walk, Asymptotic Laws and Methods in Stochastics: Festschrift in Honor of Miklós Csörgő, Springer, Berlin, to appear (accepted for publication), 2015
Csiszár V; Fegyverneki T; Móri TF: Explicit multivariate bounds of Chebyshev type, Annales Univ. Sci. Budapest, Sect. Comp. 42: 109-125, 2014
Backhausz Á; Móri TF: Asymptotics of a renewal-like recursion and an integral equation, Applicable Analysis and Discrete Mathematics 8: 200-223, 2014
Backhausz Á; Móri TF: Asymptotic properties of a random graph with duplications, Journal of Applied Probability 52: 375-390, 2015
Csáki E; Csörgő M; Földes A; Révész P: Some limit theorems for heights of random walks on a spider, Journal of Theoretical Probability (accepted for publication), 2016
Csáki E; Csörgő M; Kulik R: Strong approximations for long memory sequences based partial sums, counting and their Vervaat processes, Periodica Mathematica Hungarica (accepted for publication), 2016
Backhausz Á; Móri TF: Further properties of a random graph with duplications and delations, Stochastic Models 32 (accepted for publication), 2016
Csáki E; Csörgő M; Földes A; Révész P: Two-dimensional anisotropic random walks: fixed versus random column configurations for transport phenomena, Journal of Statistical Physics, submitted; decision: revisions needed; arXiv: 1709.10292v1 [math.PR], 2018





 

Events of the project

 
2014-01-09 15:53:02
Résztvevők változása




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