Large deviations for Markov chains

by Acosta, Alejandro D. de

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Title Statements

Full title :Large deviations for Markov chains / Alejandro D. de Acosta

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."

Edition Statements

Publication Date:2022

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge
Language:eng
Publication Date:2022

The Physical Object

Description:xii, 249 p. ; : 24 cm

Edition Identifiers

ISBN:9781316511893, 1316511898
oclc:on1361669936
Dewey Decimal:519.233

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.