Recurrence and invariant measure of Markov chains in double-infinite random environments  

作　　者：李应求 

出　　处：《Science China Mathematics》2001年第10期1294-1299,共6页中国科学：数学（英文版）

基　　金：the Natural Science Foundation of Hunan Province (Grant No. 99JJY2001) ; Hunan Provincial Foundation for Young and Middleaged People (Grant No. 00JJEY2141) .

摘　　要：The concepts of π-irreduciblity, recurrence and transience are introduced into the research field of Markov chains in random environments.That a π-irreducible chain must be either recurrent or transient is proved, a criterion is shown for recurrent Markov chains in double-infinite random environments, the existence of invariant measure of π-irreducible chains in double-infinite environments is discussed,and then Orey's open-questions are partially answered.The concepts of π -irreduciblity, recurrence and transience are introduced into the research field of Markov chains in random environments. That a π -irreducible chain must be either recurrent or transient is proved, a criterion is shown for recurrent Markov chains in double-infinite random environments, the existence of invariant measure of π -irreducible chains in double-infinite environments is discussed, and then Orey’s open-questions are partially answered.

关 键 词：double-infinite environment Markov chain RECURRENCE TRANSIENCE irreduciblity invariant measure 

分 类 号：O211.6[理学—概率论与数理统计]