Some Researches On Problems Of Markov Chains In Random Environments

Markov chains in random environments and the related problems are studied in this paper,and Markov chains in random environments and their ergodicity,Markov chains in random environments indexed by Cayley's trees,Markov chains in Markovian environments indexed by Cayley's trees and their relative entropy densities are discussed.By using existing research results and methods of the strong limit theorems and ergodic properties for non-homogeneous Markov chains,Markov chains in random environments and Markov chains indexed by Cayley's trees,some conclusions are promoted and then proved in detail.The generalized conclusions can be used to model the more general cases.This paper is divided into five chapters.In the first chapter,research background and status are presented,and the main conclusions are briefly introduced.In the second chapter,a strong limit theorem of moving average for a trifunction of a Markov chain in a random environment is studied.The technique of the proof is to make a likelihood ratio with a parameter.In the third chapter,some strong limit theorems,strong laws of large numbers and strong laws of deviation of Markov chains in Markovian environments indexed by Cayley's trees are obtained.In the fourth chapter,relative entropy densities of Markov chains in Markovian environments indexed by Cayley's trees and their asymptotic equipartition properties(AEP)are discussed.In the fifth chapter,the C-strong ergodicity of Markov chains in random environments is discussed and some judgment theorems of Markov chains in random environments are given.