The Limit Theorems for Function of Markov Chains in the Environment of Single Infinite Markovian Systems

Zhanfeng Li, Min Huang, Xiaohua Meng and Xiangyu Ge

Mathematical Problems in Engineering, 2020, vol. 2020, 1-11

Abstract:

This paper is intended to study the limit theorem of Markov chain function in the environment of single infinite Markovian systems. Moreover, the problem of the strong law of large numbers in the infinite environment is presented by means of constructing martingale differential sequence for the measurement under some different sufficient conditions. If the sequence of even functions satisfies different conditions when the value ranges of are different, we have obtained SLLN for function of Markov chain in the environment of single infinite Markovian systems. In addition, the paper studies the strong convergence of the weighted sums of function for finite state Markov Chains in single infinitely Markovian environments. Although the similar conclusions have been carried out, the difference results performed by previous scholars are that we give weaker different sufficient conditions of the strong convergence of weighted sums compared with the previous conclusions.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:8175723

DOI: 10.1155/2020/8175723

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