随机环境中马氏链状态的常返性与暂留性  

Recurrence and trancience of states for Markov chains in random environments

作　　者：费时龙[1] 任敏 

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《高校应用数学学报（A辑）》2011年第2期187-194,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10726075);安徽省教育厅自然科学研究项目(KJ2011B176);宿州学院硕士科研启动基金(2008yss20)

摘　　要：给出了随机环境中马氏链状态必然是弱常返或强暂留的几个充分条件,引入了状态周期的概念,得到类似于经典马氏链状态周期的几个性质.引入了随机环境中马氏链状态的几个数字特征,给出了随机环境中马氏链状态是弱常返与强常返等价的充分条件,利用这一条件可以说明相关文献所出现的错误结论.Several sufficient conditions that the state is always weak recurrence or strong tran-cience are given and state period which is the same as the state period of Markov chains is introduced and its properties are studied.Several numerical characteristic are introduced,then the sufficient con-dition that the state with weak recurrence is strong recurrence are given.Using this property,some wrong assertions are also presented.

关 键 词：随机环境中马氏链 周期 弱常返 强常返 强暂留 

分 类 号：O211.62[理学—概率论与数理统计]