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02668aam a22003738i 4500 001 1B401CEE803411ED944134D030ECA4DB 003 SILO 005 20221220010056 008 220202t20222022enk b 001 0 eng 010 $a 2021062728 020 $a 1316511898 020 $a 9781316511893 035 $a (OCoLC)1290429511 040 $a DLC $b eng $e rda $c DLC $d UKMGB $d OCLCF $d IPS $d NUI $d SILO 042 $a pcc 050 00 $a QA3 $b .C3 no.229 100 1 $a Acosta, Alejandro D. de, $d 1941- $e author. 245 10 $a Large deviations for Markov chains / $c Alejandro D. de Acosta, Case Western Reserve University. 264 1 $a Cambridge, United Kingdom ; $b Cambridge University Press, $c 2022. 300 $a xii, 249 pages ; $c 24 cm. 490 0 $a Cambridge tracts in mathematics ; $v 229 504 $a Includes bibliographical references (pages 244-246) and indexes. 505 0 $a 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. 520 $a "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"--Provided by publisher. 650 0 $a Large deviations. 650 0 $a Markov processes. 650 7 $a Large deviations. $2 fast $0 (OCoLC)fst00992659 650 7 $a Markov processes. $2 fast $0 (OCoLC)fst01010347 776 08 $i ebook version : $z 9781009063357 773 18 $w 990007725630202771 $g no:31858072858461 830 0 $a Cambridge tracts in mathematics ; $v 229. 941 $a 1 952 $l OVUX522 $d 20231117013952.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=1B401CEE803411ED944134D030ECA4DBInitiate Another SILO Locator Search