A strong limit theorem for the average of ternary functions of Markov chains in bi-infinite random environments

Liu Wei; Ma Chaoqun; Li Yingqiu; Wang Suming

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A strong limit theorem for the average of ternary functions of Markov chains in bi-infinite random environments

机译：双无限随机环境中马氏链平均三元函数的强极限定理

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摘要

We consider strong limit theorems for Markov chains in bi-infinite random environments. We first give a new proof of a strong limit theorem of Liu and Yang (1995) on the average of functions of non-homogeneous Markov chains by constructing a nonnegative martingale. As corollaries, for a Markov chain in a bi-infinite random environment, we obtain strong limit theorems for the conditional relative entropy and for the number of times that the Markov chain and related processes reach a given point. (C) 2015 Elsevier B.V. All rights reserved.

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《Statistics & Probability Letters》 |2015年第null期|共7页
作者
Liu Wei; Ma Chaoqun; Li Yingqiu; Wang Suming;
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正文语种 eng
中图分类概率论（几率论、或然率论）;
关键词
Bi-infinite random environment; Markov chain; Strong limit; Conditional relative entropy density;

机译：双无限随机环境;马尔可夫链;强极限;条件相对熵密度;

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1. A strong limit theorem for the average of ternary functions of Markov chains in bi-infinite random environments [J] . Liu Wei, Ma Chaoqun, Li Yingqiu, Statistics & Probability Letters . 2015,第Null期

机译：双无限随机环境中马氏链平均三元函数的强极限定理
2. A type of limit theorems for random truncated functions Sequence of mth-order nonhomogeneous markov chains on Generalized random selection systems (pp. 60-75) [J] . Kangkang Wang, Decai Zong, Hui Ye Azerbaijan Journal of Mathematics . 2013,第1期

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3. The Limit Theorems for Function of Markov Chains in the Environment of Single Infinite Markovian Systems [J] . Zhanfeng Li, Min Huang, Xiaohua Meng, Mathematical Problems in Engineering: Theory, Methods and Applications . 2020,第1期

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4. Some Strong Limit Theorems relative to the Geometric Average of Random Transition Probabilities of Nonhomogenemous Markov Chains Indexed by a Tree [C] . Huashan Wang, Weiguo Yang, Zhiyan Shi International Workshop on Computer Science and Engineering . 2009

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6. Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains [O] . Natan T’Joens, Jasper De Bock -1

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7. Some strong limit theorems for nonhomogeneous Markov chains indexed by controlled trees [O] . 2016

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8. LIMIT THEOREMS FOR TRANSIENT MARKOV CHAINS [R] . Port, Sidney C. 1966

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A strong limit theorem for the average of ternary functions of Markov chains in bi-infinite random environments

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