关于树指标二阶齐次马氏链的等价定义

The Equivalent Definition of Second-Order T-indexed Markov Chains

树指标随机过程是近年来概率论的研究方向之一,已引起了概率论、物理学、计算机等学科的广泛关注,国内外关于树指标随机过程的研究已经取得了一定的成果.树指标随机过程中的一类重要的模型就是树指标马氏链.Benjiamini和Peres首先给出了树指标马氏链的定义.杨卫国、陈晓雪和王豹给出了树指标一阶马氏链的等价定义.杨卫国等又研究了树指标马氏链强极限定理.为了更有效的研究树指标随机过程,本文给出树指标二阶齐次马氏链的等价定义,并证明其等价性.

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.