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Large deviations for Markov chains

Acosta, Alejandro D. de.

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Large deviations for Markov chains

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Large deviations for Markov chains/ Alejandro D. de Acosta, Case Western Reserve University.
作者:	Acosta, Alejandro D. de.
出版者:	Cambridge, United Kingdom ; New York, NY :Cambridge University Press, : 2022.,
面頁冊數:	xii, 249 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 19 Aug 2022).
標題:	Large deviations. -
電子資源:	https://doi.org/10.1017/9781009053129
ISBN:	9781009053129

Large deviations for Markov chains
Acosta, Alejandro D. de.

Large deviations for Markov chains[electronic resource] /Alejandro D. de Acosta, Case Western Reserve University. - Cambridge, United Kingdom ; New York, NY :Cambridge University Press,2022. - xii, 249 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;229. - Cambridge tracts in mathematics ;229..

Title from publisher's bibliographic system (viewed on 19 Aug 2022).

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.

ISBN: 9781009053129Subjects--Topical Terms:

646454
Large deviations.

LC Class. No.: QA273.67 / .A265 2022

Dewey Class. No.: 519.233

Large deviations for Markov chains
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490 1 $a Cambridge tracts in mathematics ; $v 229
500 $a Title from publisher's bibliographic system (viewed on 19 Aug 2022).
520 $a 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.
650 0 $a Large deviations. $3 646454
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830 0 $a Cambridge tracts in mathematics ; $v 229. $3 3645937
856 4 0 $u https://doi.org/10.1017/9781009053129