Large deviations for Markov chains /

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Bibliographic Details
Author / Creator:	Acosta, Alejandro D. de, 1941- author.
Imprint:	Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2022. ©2022
Description:	xii, 249 pages : illustrations ; 24 cm.
Language:	English
Series:	Cambridge tracts in mathematics ; 229 Cambridge tracts in mathematics ; 229.
Subject:	Large deviations. Markov processes. Large deviations. Markov processes.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12831400

Hidden Bibliographic Details
ISBN:	9781316511893 1316511898 9781009053129 9781009063357
Notes:	Includes bibliographical references (pages 244-246) and indexes.
Summary:	"The purpose of this book is to study 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 measure. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant measure. 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"--
Other form:	ebook version : 9781009063357

Table of Contents:

Introduction
Lower bounds and a property of lambda
Upper bounds I
Identification and reconciliation of rate functions
Necessary conditions - bounds on the rate function, invariant measures, irreducibility and recurrence
Upper bounds II - equivalent analytic conditions
Upper bounds III - sufficient conditions
The large deviations principle for empirical measures
The case when S is countable and P is matrix irreducible
Examples
Large deviations for vector-valued additive functionals.

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