The Classification And Property Of States For Markov Chains In Random Environments

In this thesis, the classification and property of States for Markov Chains in random environments are studied. It can be divided into three chapters.In the second chapter, several concepts, such as strong communication, period, etc, are introduced and their properties are discussed; we give several sufficient conditions that the state must be transience or recurrence; then the sufficient condition that the weak recurrence state is always strong recurrence is given. Using these properties, some wrong assertions are also presented; we obtain the decomposition of the state space.In the third chapter, we study some properties about the random matrices, these properties are used to obtain the results on direct convergence of products of random matrices.