?
On the kernel of the covariance operator for Markov semigroups
Applicable Analysis. 2015.
Molchanov S., Whitmeyer J.
-
Priority areas:
mathematics
Language:
English
Keywords: Markov chainscentral limit theoremцентральная предельная теоремамарковские цепиcovariance operatorковариационный оператор
Publication based on the results of:
Bufetov A. I., Mkrtchyan S., Scherbina M. et al., / Cornell University. Series math "arxiv.org". 2013. No. 1301.0342.
We show that beta ensembles in Random Matrix Theory with generic real analytic potential have the asymptotic equipartition property. In addition, we prove a Central Limit Theorem for the density of the eigenvalues of these ensembles. ...
Added: February 21, 2013
Molchanov S., Panov V., Stochastics-An International Journal of Probability and Stochastic Processes 2019 Vol. 91 No. 5 P. 754-772
In this paper, we consider limit laws for the model, which is a generalisation of the random energy model (REM) to the case when the energy levels have the mixture distribution. More precisely, the distribution of the energy levels is assumed to be a mixture of two normal distributions, one of which is standard normal, ...
Added: November 19, 2018
Panov V., Statistics and Probability Letters 2017 Vol. 129 P. 379-386
In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level depend on the number of summands. The aim of this research is to characterize the limiting distributions ...
Added: July 10, 2017
Panov V., / Cornell University. Series arXiv "math". 2017. No. 1703.10463.
In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level depend on the number of summands. The aim of this research is to characterize the limiting distributions ...
Added: March 31, 2017
Bezhaeva Z., Куликов В. Л., Олехова Е. Ф. et al., Труды Математического института им. В.А. Стеклова РАН 2017 Т. 297 С. 38-45
We define an invariant Erdős measure on the compact abelian group of A-adic integers. We also define an A-invariant Erdős measure on the n-dimensional torus. We show the connection between these invariant measures and functions of countable stationary Markov chains. ...
Added: September 7, 2017
Gribkova N., Probability and Mathematical Statistics 2017 Vol. 37 No. 1 P. 101-118
In this paper, we propose a new approach to the investigation of asymptotic properties of trimmed L-statistics and we apply it to the Cramér type large deviation problem. Our results can be compared with those in Callaert et al. (1982) – the first and, as far as we know, the single article where some results ...
Added: February 28, 2020
Konakov V., Kozhina A., Menozzi S., ESAIM: Probability and Statistics 2017 Vol. 21 P. 88-112
We study the sensitivity of the densities of non degenerate diffusion processes and related Markov Chains with respect to a perturbation of the coefficients. Natural applications of these results appear in models with misspecified coefficients or for the investigation of the weak error of the Euler scheme with irregular coefficients. ...
Added: April 14, 2017
Chebotarev A., Долгопрудный : Физтех-полиграф, 2010
Предисловие.
Теория вероятностей возникла в XVI--XVII веках как раздел математики, объясняющий причины выигрыша или проигрыша в азартных играх. Участие знаменитых ученых потребовалось для анализа игровых стратегий и объяснения ряда фактов отнюдь не очевидных с точки зрения здравого смысла. Вероятностные методы описания окружающей реальности остаются актуальными и сейчас, более того, сложность рассматриваемых систем достигла планетарного масштаба. Стохастические ...
Added: December 28, 2013
Shchegolev A., Управление большими системами: сборник трудов 2023 № 102 С. 5-14
The class of nonlinear Markov processes is characterized by the dependence of the current state of the process on its current distribution in addition to the dependence on the previous state. Due to this feature, these processes are characterized by complex limit behavior and ergodic properties, for which the usual criteria for Markov processes are ...
Added: June 12, 2023
Goetze F., Naumov A.A., Tikhomirov A., Bernoulli: a journal of mathematical statistics and probability 2017 Vol. 23 No. 4B P. 3067-3113
In this paper we consider the product of two independent random matrices X^(1) and X^(2). Assume that X_{jk}^{(q)},1\le j,k \le n,q=1,2,, are i.i.d. random variables with \EX_{jk}^{q}=0, VarX_{jk}^{(q)}=1/ Denote by s_1(W),…,s_n(W) the singular values of W:=n^{-1}X^(1)X^(2). We prove the central limit theorem for linear statistics of the squared singular values s_1^2(W),…,s_n^2(W) showing that the limiting variance depends on \kappa_4:=\E(X_{11}^{(1)})^4−3. ...
Added: April 28, 2018
Igor Kheifets, Saikkonen P., Econometric Reviews 2020 Vol. 39 No. 39 P. 407-414
Smooth transition autoregressive models are widely used to capture nonlinearities in univariate and multivariate time series. Existence of stationary solution is typically assumed, implicitly or explicitly. In this paper we describe conditions for stationarity and ergodicity of vector STAR models. The key condition is that the joint spectral radius of certain matrices is below 1, ...
Added: February 23, 2021
Sawada T., Frontiers in Psychology 2021 Vol. 12 Article 762418
This study describes how the conditions in the Central Limit theorem (CLT) are usually not satisfied in empirical Psychological studies by comparing the formulation of the CLT with a common experimental procedure used in empirical Psychological studies. This explains why the CLT cannot assure that the population follows a normal distribution no matter how large ...
Added: November 9, 2021
Konakov V., Mammen E., / Cornell University. Series arXiv "math". 2023. No. 2304.10673.
The Robbins-Monro algorithm is a recursive, simulation-based stochastic procedure to approximate the zeros of a function that can be written as an expectation. It is known that under some technical assumptions, Gaussian limit distributions approximate the stochastic performance of the algorithm. Here, we are interested in strong approximations for Robbins-Monro procedures. The main tool for ...
Added: April 24, 2023
Bobkov S., Ulyanov V. V., Theory of Probability and Its Applications 2022 Vol. 66 No. 4 P. 537-549
We give a short overview of the results related to the refined forms of the central limit theorem, with a focus on independent integer-valued random variables (r.v.'s). In the independent and non-identically distributed (non-i.i.d.) case, an approximation is then developed for the distribution of the sum by means of the Chebyshev--Edgeworth correction containing the moments ...
Added: February 22, 2022
Belomestny D., Moulines E., Samsonov S., Statistics and Computing 2022 Vol. 32 No. 1 Article 16
In this paper, we propose an efficient variance reduction approach for additive functionals of Markov chains relying on a novel discrete-time martingale representation. Our approach is fully non-asymptotic and does not require the knowledge of the stationary distribution (and even any type of ergodicity) or specific structure of the underlying density. By rigorously analyzing the ...
Added: August 31, 2020
Konakov V., Mammen E., Bernoulli: a journal of mathematical statistics and probability 2005 Vol. 11 No. 4 P. 591-641
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. We prove Edgeworth-type expansions of order o(n-1-δ),δ>0, for transition densities. For this purpose we apply the parametrix method to represent the transition density as a functional of densities of sums of independent and identically distributed variables. Then we apply Edgeworth expansions ...
Added: December 4, 2012
Pankov A., Goryainova E. R., Жерносек А. И., М. : МАИ, 2013
Данное учебное пособие предназначено для методического обеспечения цикла лабораторных работ по курсу «Теория вероятностей и математическая статистика», «Статистические методы в социологии и экономике». Описание каждой лабораторной работы содержит следующие разделы: название и цель работы; теоретические сведения; порядок выполнения работы; контрольные вопросы. Первые две лабораторные работы посвящены предварительному статистическому анализу, третья – экспериментальной проверке центральной предельной ...
Added: July 11, 2013
Olshanski G., Selecta Mathematica, New Series 2021 Vol. 27 Article 41
Using Okounkov’s q-integral representation of Macdonald polynomials we construct an infinite sequence Ω1,Ω2,Ω3,… of countable sets linked by transition probabilities from Ω𝑁 to Ω𝑁−1 for each 𝑁=2,3,…. The elements of the sets Ω𝑁 are the vertices of the extended Gelfand–Tsetlin graph, and the transition probabilities depend on the two Macdonald parameters, q and t. These ...
Added: June 4, 2021
Konakov V., Mammen E., Probability Theory and Related Fields 2009 Vol. 143 No. 1 P. 137-176
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Second order Edgeworth type expansions for transition densities are proved. The paper differs from recent results in two respects. We allow nonhomogeneous diffusion limits and we treat transition densities with time lag converging to zero. Small time asymptotics are motivated by ...
Added: December 4, 2012
Кибзун А., Goryainova E. R., Наумов А. В., М. : Физматлит, 2014
Учебник предназначен для начального ознакомления с основами теории вероятностей и математической статистики и развития навыков решения практических задач.
Большое внимание уделено краткости изложения полного курса «Теории вероятностей и математической статистики», состоящего из теоретического и практического материала. Структура изложения максимально приближена к лекционным и практическим занятиям. Книга может одновременно играть роль учебника, задачника и справочника.
Учебник предназначен для ...
Added: December 18, 2014
Nikitin Y. Y., Petrov V. V., Zaitsev A. Y. et al., Vestnik of the St. Petersburg University: Mathematics 2018 Vol. 51 No. 2 P. 201-232
This is the first in a series of reviews devoted to the scientific achievements of the Leningrad–St. Petersburg school of probability and statistics in the period from 1947 to 2017. It is devoted to limit theorems for sums of independent random variables—a traditional subject for St. Petersburg. It refers to the classical limit theorems: the ...
Added: October 1, 2019
Bressaud X., Bufetov A.I., Hubert P., Proceedings of the London Mathematical Society 2014 Vol. 109 No. 2 P. 483-522
Deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of modulus 1. The functions γ we consider are the corresponding eigenfunctions. In Theorem 1.1, we prove that the limit inferior of the ergodic sums (n,γ(x_0)+⋯+γ(x_{n−1})) n∈N is bounded for every point x in the phase space. In Theorem ...
Added: October 23, 2014
Konakov V., Mammen E., Probability Theory and Related Fields 2000 Vol. 117 No. 4 P. 551-587
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition
densities are proved. ...
Added: October 15, 2012
Blank M., Discrete and Continuous Dynamical Systems 2021 Vol. 41 No. 4 P. 1649-1665
We study qualitative properties of the set of recurrent points of
finitely generated free semigroups of measurable maps. In the case of a single
generator the classical Poincare recurrence theorem shows that these properties are closely related to the presence of an invariant measure. Curious, but
otherwise it turns out to be possible that almost all points are ...
Added: October 21, 2020