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SOME LIMIT THEOREMS OF DELAYED AVERAGES FOR COUNTABLE NONHOMOGENEOUS MARKOV CHAINS

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  24 September 2019

Pingping Zhong ,
Weiguo Yang ,
Zhiyan Shi Open the ORCID record for Zhiyan Shi [Opens in a new window]  and
Yan Zhang
Pingping Zhong
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang212013, China E-mail: shizhiyan1984@126.comJingjiang College of Jiangsu University, Zhenjiang 212013, China
Weiguo Yang
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang212013, China E-mail: shizhiyan1984@126.comJingjiang College of Jiangsu University, Zhenjiang 212013, China
Zhiyan Shi
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang212013, China E-mail: shizhiyan1984@126.comJingjiang College of Jiangsu University, Zhenjiang 212013, China
Yan Zhang
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang212013, China E-mail: shizhiyan1984@126.comJingjiang College of Jiangsu University, Zhenjiang 212013, China
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Abstract

The purpose of this paper is to establish some limit theorems of delayed averages for countable nonhomogeneous Markov chains. The definition of the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for countable nonhomogeneous Markov chains is introduced first. Then a theorem about the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for the nonhomogeneous Markov chains is established, and its applications to the information theory are given. Finally, the strong law of large numbers of delayed averages of bivariate functions for countable nonhomogeneous Markov chains is proved.

Keywords

countable nonhomogeneous Markov chainsgeneralized C-strong ergodicitystrong law of large numbers of delayed averages

MSC classification

Primary: 60G60: Random fields
Secondary: 60F15: Strong theorems
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 2 , April 2021 , pp. 297 - 315
Copyright
Copyright © Cambridge University Press 2019

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