Local Limit Theorems For Inhomogeneous Markov Chains
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Local Limit Theorems For Inhomogeneous Markov Chains
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Author : Dmitry Dolgopyat
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
Local Limit Theorems For Inhomogeneous Markov Chains written by Dmitry Dolgopyat and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.
This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.
Limit Theorems For Markov Chains And Stochastic Properties Of Dynamical Systems By Quasi Compactness
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Author : Hubert Hennion
language : en
Publisher: Springer
Release Date : 2003-07-01
Limit Theorems For Markov Chains And Stochastic Properties Of Dynamical Systems By Quasi Compactness written by Hubert Hennion and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.
The usefulness of from the of techniques perturbation theory operators, to kernel for limit theorems for a applied quasi-compact positive Q, obtaining Markov chains for stochastic of or dynamical by describing properties systems, of Perron- Frobenius has been demonstrated in several All use a operator, papers. these works share the features the features that must be same specific general ; used in each stem from the nature of the functional particular case precise space where the of is and from the number of quasi-compactness Q proved eigenvalues of of modulus 1. We here a functional framework for Q give general analytical this method and we the aforementioned behaviour within it. It asymptotic prove is worth that this framework is to allow the unified noticing sufficiently general treatment of all the cases considered in the literature the previously specific ; characters of model translate into the verification of of simple hypotheses every a functional nature. When to Markov kernels or to Perr- applied Lipschitz Frobenius associated with these statements rise operators expanding give maps, to new results and the of known The main clarify proofs already properties. of the deals with a Markov kernel for which 1 is a part quasi-compact Q paper of modulus 1. An essential but is not the simple eigenvalue unique eigenvalue element of the work is the of the of peripheral Q precise description spectrums and of its To conclude the the results obtained perturbations.
Limit Theorems For Markov Chains And Stochastic Properties Of Dynamical Systems By Quasi Compactness
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Author : Hubert Hennion
language : en
Publisher:
Release Date : 2014-01-15
Limit Theorems For Markov Chains And Stochastic Properties Of Dynamical Systems By Quasi Compactness written by Hubert Hennion and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Limit Theorems For Functionals Of Ergodic Markov Chains With General State Space
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Author : Xia Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Limit Theorems For Functionals Of Ergodic Markov Chains With General State Space written by Xia Chen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This book is intended for graduate students and research mathematicians working probability theory and statistics.
Limit Theorems On Large Deviations For Markov Stochastic Processes
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Author : A.D. Wentzell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Limit Theorems On Large Deviations For Markov Stochastic Processes written by A.D. Wentzell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In recent decades a new branch of probability theory has been developing intensively, namely, limit theorems for stochastic processes. As compared to classical limit theorems for sums of independent random variables, the generalizations are going here in two directions simultaneously. First, instead of sums of independent variables one considers stochastic processes belonging to certain broad classes. Secondly, instead of the distribution of a single sum - the distribution of the value of a stochastic process at one (time) point - or the joint distribution of the values of a process at a finite number of points, one considers distributions in an infinite-dimensional function space. For stochastic processes constructed, starting from sums of independent random variables, this is the same as considering the joint distribution of an unboundedly increasing number of sums.
Introduction To Ergodic Rates For Markov Chains And Processes
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Author : Kulik, Alexei
language : en
Publisher: Universitätsverlag Potsdam
Release Date : 2015-10-20
Introduction To Ergodic Rates For Markov Chains And Processes written by Kulik, Alexei and has been published by Universitätsverlag Potsdam this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-20 with Mathematics categories.
The present lecture notes aim for an introduction to the ergodic behaviour of Markov Processes and addresses graduate students, post-graduate students and interested readers. Different tools and methods for the study of upper bounds on uniform and weak ergodic rates of Markov Processes are introduced. These techniques are then applied to study limit theorems for functionals of Markov processes. This lecture course originates in two mini courses held at University of Potsdam, Technical University of Berlin and Humboldt University in spring 2013 and Ritsumameikan University in summer 2013. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.
Journal Of Research Of The National Bureau Of Standards
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Author : United States. National Bureau of Standards
language : en
Publisher:
Release Date : 1963
Journal Of Research Of The National Bureau Of Standards written by United States. National Bureau of Standards and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Mathematical physics categories.
Finite Markov Processes And Their Applications
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Author : Marius Iosifescu
language : en
Publisher: Courier Corporation
Release Date : 2007-06-05
Finite Markov Processes And Their Applications written by Marius Iosifescu and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-05 with Mathematics categories.
Self-contained treatment covers both theory and applications. Topics include the fundamental role of homogeneous infinite Markov chains in the mathematical modeling of psychology and genetics. 1980 edition.
Limit Theorems For The Range Of Markov Chains
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Author : Björn Palmgren
language : en
Publisher:
Release Date : 1981
Limit Theorems For The Range Of Markov Chains written by Björn Palmgren and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Markov processes categories.
Uniform Limit Theorems For Markov Chains
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Author : Shlomo Levental
language : en
Publisher:
Release Date : 1986
Uniform Limit Theorems For Markov Chains written by Shlomo Levental and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.