Uniform Limit Theorems For Markov Chains

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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.

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 Of Probability Theory

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Author : Yu.V. Prokhorov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Limit Theorems Of Probability Theory written by Yu.V. Prokhorov 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 2013-03-14 with Mathematics categories.

This book consists of five parts written by different authors devoted to various problems dealing with probability limit theorems. The first part, "Classical-Type Limit Theorems for Sums ofIndependent Random Variables" (V.v. Petrov), presents a number of classical limit theorems for sums of independent random variables as well as newer related results. The presentation dwells on three basic topics: the central limit theorem, laws of large numbers and the law of the iterated logarithm for sequences of real-valued random variables. The second part, "The Accuracy of Gaussian Approximation in Banach Spaces" (V. Bentkus, F. G6tze, V. Paulauskas and A. Rackauskas), reviews various results and methods used to estimate the convergence rate in the central limit theorem and to construct asymptotic expansions in infinite-dimensional spaces. The authors con fine themselves to independent and identically distributed random variables. They do not strive to be exhaustive or to obtain the most general results; their aim is merely to point out the differences from the finite-dimensional case and to explain certain new phenomena related to the more complex structure of Banach spaces. Also reflected here is the growing tendency in recent years to apply results obtained for Banach spaces to asymptotic problems of statistics.

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.

Some Limit Theorems For Markov Chains And Related Occupancy Problems

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Author : Burton Herbert Singer
language : en
Publisher:
Release Date : 1967

Some Limit Theorems For Markov Chains And Related Occupancy Problems written by Burton Herbert Singer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Markov processes categories.

General Irreducible Markov Chains And Non Negative Operators

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Author : Esa Nummelin
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-03

General Irreducible Markov Chains And Non Negative Operators written by Esa Nummelin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-03 with Mathematics categories.

Presents the theory of general irreducible Markov chains and its connection to the Perron-Frobenius theory of nonnegative operators.

Limit Theorems For Randomly Stopped Stochastic Processes

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Author : Dmitrii S. Silvestrov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Limit Theorems For Randomly Stopped Stochastic Processes written by Dmitrii S. Silvestrov 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.

Limit theorems for stochastic processes are an important part of probability theory and mathematical statistics and one model that has attracted the attention of many researchers working in the area is that of limit theorems for randomly stopped stochastic processes. This volume is the first to present a state-of-the-art overview of this field, with many of the 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. A survey of the literature and an extended bibliography of works in the area are also provided. The coverage is thorough, streamlined and arranged according to difficulty for use as an upper-level text if required. It is an essential reference for theoretical and applied researchers in the fields of probability and statistics that will contribute to the continuing extensive studies in the area andremain relevant for years to come.

Statistical Inference For Piecewise Deterministic Markov Processes

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Author : Romain Azais
language : en
Publisher: John Wiley & Sons
Release Date : 2018-07-30

Statistical Inference For Piecewise Deterministic Markov Processes written by Romain Azais and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-30 with Mathematics categories.

Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance... Such processes are defined by a deterministic motion punctuated by random jumps at random times, and offer simple yet challenging models to study. Nevertheless, the issue of statistical estimation of the parameters ruling the jump mechanism is far from trivial. Responding to new developments in the field as well as to current research interests and needs, Statistical inference for piecewise-deterministic Markov processes offers a detailed and comprehensive survey of state-of-the-art results. It covers a wide range of general processes as well as applied models. The present book also dwells on statistics in the context of Markov chains, since piecewise-deterministic Markov processes are characterized by an embedded Markov chain corresponding to the position of the process right after the jumps.

Strong Stable Markov Chains

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Author : N. V. Kartashov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-01-14

Strong Stable Markov Chains written by N. V. Kartashov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-14 with Mathematics categories.

No detailed description available for "Strong Stable Markov Chains".

Markov Chains And Stochastic Stability

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Author : Sean P. Meyn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Markov Chains And Stochastic Stability written by Sean P. Meyn 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 Technology & Engineering categories.

Markov Chains and Stochastic Stability is part of the Communications and Control Engineering Series (CCES) edited by Professors B.W. Dickinson, E.D. Sontag, M. Thoma, A. Fettweis, J.L. Massey and J.W. Modestino. The area of Markov chain theory and application has matured over the past 20 years into something more accessible and complete. It is of increasing interest and importance. This publication deals with the action of Markov chains on general state spaces. It discusses the theories and the use to be gained, concentrating on the areas of engineering, operations research and control theory. Throughout, the theme of stochastic stability and the search for practical methods of verifying such stability, provide a new and powerful technique. This does not only affect applications but also the development of the theory itself. The impact of the theory on specific models is discussed in detail, in order to provide examples as well as to demonstrate the importance of these models. Markov Chains and Stochastic Stability can be used as a textbook on applied Markov chain theory, provided that one concentrates on the main aspects only. It is also of benefit to graduate students with a standard background in countable space stochastic models. Finally, the book can serve as a research resource and active tool for practitioners.