双无限随机环境中马氏链的瞬时性与不变函数

TRANSIENCE AND INVARIANT FUNCTIONS FOR MARKOV CHAINS IN DOUBLY INFINITE RANDOM ENVIRONMENT

在随机环境中马氏链的研究领域,引入了一类π-不可约、常返和瞬时性的概念,给出了π-不可约链是瞬时链的一个充要条件,引入了双无限随机环境中马氏链不变函数的概念,讨论了它们的存在性及基本性质。最后,利用不变函数的性质,给出了π-不可约链是瞬时链的一个判别准则,此准则与不变函数有关。

In investigate field of Markov chains in random environments, the concepts for π-irreduciblity, recurrence and transience of Markov chains in doubly infinite random environment are introduced. The sufficient and necessary conditions that π-irreducible Markov chains in doubly infinite random environment are transient is given. The concepts for invariant functions of Markov chains in doubly infinite random environment are introduced. Their existence and basic properties are studied. Using these properties, a criterion that π-irreducible Markov chains in doubly infinite random environment are transient is given.