The Equivalent Definition of Second-Order T-indexed Markov Chains
JI Jin-l · College Mathematics · 2015
T-indexed stochastic processes have been one of the research directions in probability theory,which have draw wide attention of probability theory,physics,computer science and so on in recent years.There have been some works on tree-indexed stochastic processes at home and abroad.Tree-indexed Markov chain is a kind of important model of tree-indexed stochastic processes.Benjiamini and Peres firstly give the definition of Markov chains.Yang,Chen and Wang give the equivalent definition of t-indexed Markov chains.Yang have studied the strong laws of large numbers and Asymptotic Equipartition Property(AEP)for Markov chains field on trees and studied the strong limit theorem of t-indexed Markov chains.In order to study series of related problems about t-indexed stochastic processes efficiently,this paper presents the equivalent definition of second-order t-indexed Markov chains and proves the equivalence of it.