The Markov approximation of the sequences of \(N\)-valued random variables and a class of small deviation theorems.
type: Item
instance of: scholarly article
title: The Markov approximation of the sequences of \(N\)-valued random variables and a class of small deviation theorems.
zbMATH Open document ID: 1051.94005
DOI: 10.1016/S0304-4149(00)00016-8
author: Wen Liu
author: Weiguo Yang
published in: Stochastic Processes and their Applications
publication date: 2004-09-07T00:00:00Z
review text: The authors consider the sample divergence \[ h(P\mid Q)=\lim \sup _n n^{-1}\text{ln}(p_n(Y_n)/q_n(Y_n)) \] where \(Y_n\) is a random \(P\)-distributed message of length \(n\geq 1\) over a finite alphabet \(S\), \(p_n\) is the density of an \(n\)-restricted probability measure \(P\) with respect to the counting measure and \(q_n\) is similarly the density of an \(n\)-restricted Markov measure \(Q\). The authors prove a class of small deviation theorems for a class of functions \(Y_n\) using the sample divergence and an extension of a theorem of Shannon and McMillan to nonhomogeneous Markov information sources \(Y_{\infty }\).
Mathematics Subject Classification ID: 94A15
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 94A55
zbMATH DE Number: 2098344
zbMATH Keywords: sample divergence
zbMATH Keywords: Markov approximation
zbMATH Keywords: small deviations
MaRDI profile type: Publication
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full work available at URL: s0304-4149(00)00016-8
OpenAlex ID: W2171607060
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description: scientific article; zbMATH DE number 2098344