An extension of Shannon-McMillan theorem and some limit properties for nonhomogeneous Markov chains
type: Item
instance of: scholarly article
title: An extension of Shannon-McMillan theorem and some limit properties for nonhomogeneous Markov chains
zbMATH Open document ID: 0861.60042
DOI: 10.1016/0304-4149(95)00068-2
author: Wen Liu
author: Weiguo Yang
published in: Stochastic Processes and their Applications
publication date: 1996-08-05T00:00:00Z
review text: Let \((X_n, n\geq 0)\) be a Markov chain with state space \(S=(1,2,\dots,m)\) and joint distribution \(P(X_0=x_0, X_1=x_1,\dots,X_n=x_n)= P(x_0,x_1,\dots,x_n)>0\), \(x_i\in S\), \(i=1,2,\dots,n\). Then the relative entropy density \(f_n(\omega)\) is given by \(nf_n(\omega)=-\log P(X_0,X_1,\dots,X_n)\). Let \(g_k(i,j)\) be a real-valued function defined on \(S\times S\) and let \(nF_n(\omega)= \sum^n_{k=1}g_k(i,j)\). Some almost sure limit theorems have been proved for \(F_n(\omega)\), and Shannon-McMillan theorem on the entropy has been extended to a class of nonhomogeneous Markov chains.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 62B10
zbMATH DE Number: 894791
zbMATH Keywords: Markov chain
zbMATH Keywords: entropy density
zbMATH Keywords: limit theorems
zbMATH Keywords: Shannon-McMillan theorem
MaRDI profile type: Publication
full work available at URL: 0304-4149(95)00068-2
OpenAlex ID: W1987408198
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description: scientific article; zbMATH DE number 894791