关于马氏环境中马氏链的一个极限性质
A Limit Property for Non-Homogeneous Markov Chain in Markov Environments
摘要:
本文研究马氏环境中非齐次马氏链泛函的滑动平均强极限性质。通过构造一列带参数且期望为1的随机变量,利用Borel-Cantelli引理来研究随机环境中马氏链的强极限定理,得到了马氏环境中马氏链泛函滑动平均的一个强极限定理,推广了若干已有结论。
Abstract:
In this paper we discuss the strong limit properties for moving average of functions of non-ho- mogeneous Markov chain in Markov environments. By constructing a sequence of random va-riables with one parameter and take 1 as the expectation, with the aid of the classic Borel-Cantelli lemma, we study the strong limit properties of Markov chain in random environments and obtain a strong limit theorem for moving average of functions of non-homogeneous Markov chain in Markov environments. Moreover, we generalize the existing results.
参考文献
[1]
|
Cogburn, R. (1984) The Ergodic Theory of Markov Chains in Random Environments. Z.W., 66, 109-128.
|
[2]
|
Cogburn, R. (1990) On Direct Convergence and Periodicity for Transition Probabilities of Markov Chains in Random Environments. Annals of Probability, 18, 642-654. http://dx.doi.org/10.1214/aop/1176990850
|
[3]
|
Cogburn, R. (1991) On the Central Limit Theorem for Markov Chains in Random Environments. Annals of Probability, 19, 587-604. http://dx.doi.org/10.1214/aop/1176990442
|
[4]
|
李应求. 关于马氏环境中马氏链的几点注记[J]. 数学发展, 1999, 28(4): 358-360.
|
[5]
|
李应求. 状态可数的马氏环境中马氏链函数的强大数定律[M]. 数学杂志, 2003, 23(4): 484-490.
|
[6]
|
Seppalainen, T. (1994) Large Deviations for Markov Chains with Random Transitions. Annals of Probability, 22, 713- 748. http://dx.doi.org/10.1214/aop/1176988727
|
[7]
|
毕秋香, 李炜. 随机环境中马氏链的泛函极限定理[J]. 中山大学学报, 2000, 39(6): 153-156.
|
[8]
|
汪忠志, 陈文波. 随机环境中非齐次马氏链的一类强极限定理[J]. 河南科学, 2002, 20(4): 336-338.
|
[9]
|
汪忠志. 随机环境中非齐次马氏链泛函的一类强极限定理[J]. 安徽工业大学学报, 2004, 21(1): 79-82.
|
[10]
|
Wang, Z.Z. and Yang, W.G. (2015) The Generalized Entropy Ergodicity Theorem for Nonhomogeneous Markov Chains. Journal of Theoretical Probability, 1-15. http://dx.doi.org/10.1007/s10959-015-0597-9
|
[11]
|
李应求. 马氏环境中马氏链的一类强极限定理[J]. 数学进展, 2008, 37(5): 539-549.
|