Large Deviations For Markov Chains
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Large Deviations For Markov Chains
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Author : Alejandro D. de Acosta
language : en
Publisher:
Release Date : 2022-10-12
Large Deviations For Markov Chains written by Alejandro D. de Acosta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-12 with Mathematics categories.
This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.
Large Deviations For Additive Functionals Of Markov Chains
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Author : Alejandro D. de Acosta
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-03-05
Large Deviations For Additive Functionals Of Markov Chains written by Alejandro D. de Acosta 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 2014-03-05 with Mathematics categories.
Large Deviations For Stochastic Processes
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Author : Jin Feng
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-03
Large Deviations For Stochastic Processes written by Jin Feng 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 2015-02-03 with Large deviations categories.
The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.
Large Deviations
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Author : Frank Hollander
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Large Deviations written by Frank Hollander 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 2000 with Mathematics categories.
Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.
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.
Large Deviations
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Author : S. R. S. Varadhan
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-12-08
Large Deviations written by S. R. S. Varadhan 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 2016-12-08 with Large deviations categories.
The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems.
Large Deviations And Adiabatic Transitions For Dynamical Systems And Markov Processes In Fully Coupled Averaging
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Author : Yuri Kifer
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-08-07
Large Deviations And Adiabatic Transitions For Dynamical Systems And Markov Processes In Fully Coupled Averaging written by Yuri Kifer 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 2009-08-07 with Mathematics categories.
The work treats dynamical systems given by ordinary differential equations in the form $\frac{dX^\varepsilon(t)}{dt}=\varepsilon B(X^\varepsilon(t),Y^\varepsilon(t))$ where fast motions $Y^\varepsilon$ depend on the slow motion $X^\varepsilon$ (coupled with it) and they are either given by another differential equation $\frac{dY^\varepsilon(t)}{dt}=b(X^\varepsilon(t), Y^\varepsilon(t))$ or perturbations of an appropriate parametric family of Markov processes with freezed slow variables.
Large Deviations
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Author :
language : en
Publisher: Academic Press
Release Date : 1989-06-21
Large Deviations written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-06-21 with Mathematics categories.
The first four chapters of this volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).
Large Deviations And Applications
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Author : S. R. S. Varadhan
language : en
Publisher: SIAM
Release Date : 1984-01-31
Large Deviations And Applications written by S. R. S. Varadhan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-31 with Mathematics categories.
Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.
Large Deviations For Discrete Time Processes With Averaging
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Author : O. V. Gulinsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-01-14
Large Deviations For Discrete Time Processes With Averaging written by O. V. Gulinsky 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.
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