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浙江大学学报（理学版）
浙江大学学报（理学版）  2017, Vol. 44 Issue (4): 411-416    DOI: 10.3785/j.issn.1008-9497.2017.04.005
数学与计算机科学     
多重随机环境中马氏链及其强大数定律
费时龙
宿州学院 数学与统计学院, 安徽 宿州 234000
The multiple Markov chains in a random environment and the strong law of large numbers
FEI Shilong
School of Mathematics and Statistics, Suzhou University, Suzhou 234000, Anhui Province, China
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摘要： 引入了多重随机环境中的马尔科夫链模型，该模型是随机环境中马尔科夫链模型的推广，适用范围更广.给出了多重随机环境中马尔科夫链模型的2个应用背景；讨论了m重随机环境中马尔科夫链、n重随机环境中马尔科夫链、马氏链、2m维链的相互关系及性质.最后，利用得到的多重马氏链的相关性质获得了多重随机环境中马尔科夫链强大数定律成立的充分条件，推广了部分文献的结论.
关键词： 随机环境;  m重马氏链;  强大数定律    
Abstract: The model of multiple Markov chains in a random environment is introduced which is a promotion of Markov chains in a random environment with a more general application scope. Two application backgrounds of the multiple Markov chains in a random environment are given. Then, we discuss some relations and properties of the order m Markov chains and the order k Markov chains in a random environment,Markov chains, and 2m dimensional chains. At last, using the property of the multiple Markov chains in a random environment, we obtain the sufficient condition of the strong law of large numbers of the multiple Markov chains in a random environment, which are a promotion of the results from some literatures.
Key words: random environments    Markov chains with order m    strong law of large numbers
收稿日期: 2016-01-18 出版日期: 2017-12-09
CLC:  O211.62  
基金资助: 安徽省高等学校省级自然科学基金资助项目（KJ2016A770）；安徽省高校优秀青年人才支持计划重点项目（gxyqZD2016340）.
作者简介: 费时龙(1980-),ORCID:http://orcid.org/0000-0003-4352-9345,男,硕士,副教授,主要从事随机过程研究,E-mail:fsl627@sina.com.
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引用本文:

费时龙. 多重随机环境中马氏链及其强大数定律[J]. 浙江大学学报（理学版）, 2017, 44(4): 411-416.

FEI Shilong. The multiple Markov chains in a random environment and the strong law of large numbers. Journal of ZheJIang University(Science Edition), 2017, 44(4): 411-416.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.04.005    或    https://www.zjujournals.com/sci/CN/Y2017/V44/I4/411

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