绕积马氏链的状态分类

The Classification of States for Skew Product Markov Chains

该文给出了绕积马氏链的特征数和状态的定义 ,利用一般马氏链的理论讨论了随机环境中的马氏链的各种状态的特征以及各类状态之间的联系 ,还给出了在联合空间不可分解且正则本质的条件下 ,状态正则本质的充要条件 .最后举例说明了经典马氏链和随机环境中马氏链的状态的区别 .

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 on the states, such as recurrent state, strongly recurrent state, and strongly transient state, 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 indecomposable and proper essential.