随机环境中马氏链的Brunel极大遍历定理  

Brunel Ergodic Theorem of Markov Chains in Random Environments

作　　者：贾兆丽[1,2] 凌能祥[1] 

机构地区：[1]合肥工业大学数学学院,合肥230009 [2]中国科学技术大学统计与金融系,合肥230026

出　　处：《工程数学学报》2012年第6期842-846,共5页Chinese Journal of Engineering Mathematics

基　　金：中央高校基本科研业务费专项资金(2012HFXJ0043);教育部人文社科规划基金(10YJA910005)~~

摘　　要：随机环境中的马氏链是一类重要的随机过程.由于这类过程在金融、保险、计算机网络、随机服务系统等领域的广泛应用,对其理论和方法的研究,特别是其遍历性的理论和方法的研究受到很多学者的关注.本文利用单调收敛定理,在比较自然的条件下,获得了随机环境中马氏链的极大遍历性定理,推广了现有文献中的相关结果.Markov chain in random environments is an important stochastic process. Because of its widely application in finance, insurance, communication, computer network, queue theory, stochastic service system etc, many researchers have paid attention to the theory and method of Markov chains, especially its ergodic theorems. In this paper, under general conditions, we obtain the Brunel and Hopf great ergodic theorems of Markov chain in random environments by using the monotonous convergence theorem, which expand the results in the present literature.

关 键 词：随机环境 马氏链 遍历定理 单调收敛 

分 类 号：O211.62[理学—概率论与数理统计]