关键词: 随机环境中的马氏链;绕积马氏链;状态分类;随机环境

Abstract:

The main result of this paper is the classification of states on skew  product Markov chains. First of all, the authors introduce some basic concepts o n the sta tes, such as recurrent state, strongly recurrent state, and strongly transient s tate, essential state, and then give some criteria. At last, the paper provides  the necessary and  sufficient conditions for proper essential state where joint space is indecompo sable and proper essential.

Key words: Markov chains in random environments, Skew product Markov chains, Classification of states, Random environments.