Tree-Indexed Markov Chains in Random Environment and Some of Their Strong Limit Properties*

Citation:

Jing MAO,Zhiyan SHI,Bei WANG,Weiguo YANG,Zhongzhi WANG.Tree-Indexed Markov Chains in Random Environment and Some of Their Strong Limit Properties*[J].Chinese Annals of Mathematics B,2022,43(4):621~642
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Authors:

Jing MAO; Zhiyan SHI;Bei WANG;Weiguo YANG;Zhongzhi WANG

Foundation:

National Natural Science Foundation of China (Nos. 11571142,11971197, 11601191).
Abstract: In this paper, the authors first introduce the tree-indexed Markov chains in random environment, which takes values on a general state space. Then, they prove the existence of this stochastic process, and develop a class of its equivalent forms. Based on this property, some strong limit theorems including conditional entropy density are studied for the tree-indexed Markov chains in random environment.

Keywords:

Random environment, Tree-indexed Markov chains, Strong limit theorem, Conditional entropy density

Classification:

60G60, 60J10, 60F15
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