The Generalized Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree

In this paper, we study the generalized entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Firstly, by constructing a class of random variables with a parameter and the mean value of one, we establish a strong limit theorem for delayed sums of the bivariat...

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Detalles Bibliográficos
Autores principales: Shi, Zhiyan, Wang, Zhongzhi, Zhong, Pingping, Fan, Yan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8329646/
https://www.ncbi.nlm.nih.gov/pubmed/34366565
http://dx.doi.org/10.1007/s10959-021-01117-1
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author Shi, Zhiyan
Wang, Zhongzhi
Zhong, Pingping
Fan, Yan
author_facet Shi, Zhiyan
Wang, Zhongzhi
Zhong, Pingping
Fan, Yan
author_sort Shi, Zhiyan
collection PubMed
description In this paper, we study the generalized entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Firstly, by constructing a class of random variables with a parameter and the mean value of one, we establish a strong limit theorem for delayed sums of the bivariate functions of such chains using the Borel–Cantelli lemma. Secondly, we prove the strong law of large numbers for the frequencies of occurrence of states of delayed sums and the generalized entropy ergodic theorem. As corollaries, we generalize some known results.
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spelling pubmed-83296462021-08-03 The Generalized Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree Shi, Zhiyan Wang, Zhongzhi Zhong, Pingping Fan, Yan J Theor Probab Article In this paper, we study the generalized entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Firstly, by constructing a class of random variables with a parameter and the mean value of one, we establish a strong limit theorem for delayed sums of the bivariate functions of such chains using the Borel–Cantelli lemma. Secondly, we prove the strong law of large numbers for the frequencies of occurrence of states of delayed sums and the generalized entropy ergodic theorem. As corollaries, we generalize some known results. Springer US 2021-08-03 2022 /pmc/articles/PMC8329646/ /pubmed/34366565 http://dx.doi.org/10.1007/s10959-021-01117-1 Text en © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Shi, Zhiyan
Wang, Zhongzhi
Zhong, Pingping
Fan, Yan
The Generalized Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree
title The Generalized Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree
title_full The Generalized Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree
title_fullStr The Generalized Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree
title_full_unstemmed The Generalized Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree
title_short The Generalized Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree
title_sort generalized entropy ergodic theorem for nonhomogeneous bifurcating markov chains indexed by a binary tree
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8329646/
https://www.ncbi.nlm.nih.gov/pubmed/34366565
http://dx.doi.org/10.1007/s10959-021-01117-1
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