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Local Limit Theorems For Inhomogeneous Markov Chains
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Book Synopsis Local Limit Theorems for Inhomogeneous Markov Chains by : Dmitry Dolgopyat
Download or read book Local Limit Theorems for Inhomogeneous Markov Chains written by Dmitry Dolgopyat and published by Springer Nature. This book was released on 2023-07-31 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness by : Hubert Hennion
Download or read book Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness written by Hubert Hennion and published by Springer. This book was released on 2003-07-01 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Journal of Research of the National Bureau of Standards by : United States. National Bureau of Standards
Download or read book Journal of Research of the National Bureau of Standards written by United States. National Bureau of Standards and published by . This book was released on 1963 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Limit Theorems for Functionals of Ergodic Markov Chains with General State Space by : Xia Chen
Download or read book Limit Theorems for Functionals of Ergodic Markov Chains with General State Space written by Xia Chen and published by American Mathematical Soc.. This book was released on 1999 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians working probability theory and statistics.
Book Synopsis Finite Markov Processes and Their Applications by : Marius Iosifescu
Download or read book Finite Markov Processes and Their Applications written by Marius Iosifescu and published by Courier Corporation. This book was released on 2007-06-05 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Limit Theorems on Large Deviations for Markov Stochastic Processes by : A.D. Wentzell
Download or read book Limit Theorems on Large Deviations for Markov Stochastic Processes written by A.D. Wentzell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness by : Hubert Hennion
Download or read book Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness written by Hubert Hennion and published by . This book was released on 2014-01-15 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Ergodic rates for Markov chains and processes by : Kulik, Alexei
Download or read book Introduction to Ergodic rates for Markov chains and processes written by Kulik, Alexei and published by Universitätsverlag Potsdam. This book was released on 2015-10-20 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Recent Soviet Contributions to Mathematics by : Joseph P. LaSalle
Download or read book Recent Soviet Contributions to Mathematics written by Joseph P. LaSalle and published by . This book was released on 1962 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Limit Theorems for the Range of Markov Chains by : Björn Palmgren
Download or read book Limit Theorems for the Range of Markov Chains written by Björn Palmgren and published by . This book was released on 1981 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Uniform Limit Theorems for Markov Chains by : Shlomo Levental
Download or read book Uniform Limit Theorems for Markov Chains written by Shlomo Levental and published by . This book was released on 1986 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis U.S. Government Research Reports by :
Download or read book U.S. Government Research Reports written by and published by . This book was released on 1964 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ergodic Behavior of Markov Processes by : Alexei Kulik
Download or read book Ergodic Behavior of Markov Processes written by Alexei Kulik and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-11-20 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general topic of this book is the ergodic behavior of Markov processes. A detailed introduction to methods for proving ergodicity and upper bounds for ergodic rates is presented in the first part of the book, with the focus put on weak ergodic rates, typical for Markov systems with complicated structure. The second part is devoted to the application of these methods to limit theorems for functionals of Markov processes. The book is aimed at a wide audience with a background in probability and measure theory. Some knowledge of stochastic processes and stochastic differential equations helps in a deeper understanding of specific examples. Contents Part I: Ergodic Rates for Markov Chains and Processes Markov Chains with Discrete State Spaces General Markov Chains: Ergodicity in Total Variation MarkovProcesseswithContinuousTime Weak Ergodic Rates Part II: Limit Theorems The Law of Large Numbers and the Central Limit Theorem Functional Limit Theorems
Book Synopsis Nonconventional Limit Theorems And Random Dynamics by : Kifer Yuri
Download or read book Nonconventional Limit Theorems And Random Dynamics written by Kifer Yuri and published by World Scientific. This book was released on 2018-04-05 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to limit theorems for nonconventional sums and arrays. Asymptotic behavior of such sums were first studied in ergodic theory but recently it turned out that main limit theorems of probability theory, such as central, local and Poisson limit theorems can also be obtained for such expressions. In order to obtain sufficiently general local limit theorem, we develop also thermodynamic formalism type results for random complex operators, which is one of the novelties of the book. Contents: Nonconventional Limit Theorems: Stein's Method for Nonconventional Sums Local Limit Theorem Nonconventional Arrays Random Transformations Thermodynamic Formalism for Random Complex Operators: Ruelle–Perron–Frobenius Theorem via Cone Contractions Application to Random Locally Expanding Covering Maps Pressure, Asymptotic Variance and Complex Gibbs Measures Application to Random Complex Integral Operators Fiberwise Limit Theorems Readership: Advanced graduate students and researchers in probability theory and stochastic processes and dynamical systems and ergodic theory. Keywords: Limit Theorems;Nonconventional Sums;Nonconventional Arrays;Stochastic Processes;Dynamical Systems;Stein's Method;Martingale Approximation;Thermodynamic Formalism;Strong Law of Large Numbers;Central;Local and Poisson Limit TheoremsReview: Key Features: The results in the book are new and never appeared before, Prof. Yuri Kifer is a well-known researcher in probability and dynamical systems, he published several books and more than 130 papers and he initiated the research on nonconventional limit theorems in the last decade
Author :Dmitrii S. Silvestrov Publisher :Springer Science & Business Media ISBN 13 :0857293907 Total Pages :408 pages Book Rating :4.8/5 (572 download)
Book Synopsis Limit Theorems for Randomly Stopped Stochastic Processes by : Dmitrii S. Silvestrov
Download or read book Limit Theorems for Randomly Stopped Stochastic Processes written by Dmitrii S. Silvestrov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first to present a state-of-the-art overview of this field, with many results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast and technically demanding Russian literature in detail. Its coverage is thorough, streamlined and arranged according to difficulty.
Book Synopsis Lecture Notes on Limit Theorems for Markov Chain Transition Probabilities by : Steven Orey
Download or read book Lecture Notes on Limit Theorems for Markov Chain Transition Probabilities written by Steven Orey and published by . This book was released on 1971 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Compound Renewal Processes by : A. A. Borovkov
Download or read book Compound Renewal Processes written by A. A. Borovkov and published by Cambridge University Press. This book was released on 2022-06-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.
