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

Journal of Theoretical Probability ◽

10.1007/s10959-021-01117-1 ◽

2021 ◽

Author(s):

Zhiyan Shi ◽

Zhongzhi Wang ◽

Pingping Zhong ◽

Yan Fan

Keyword(s):

Markov Chains ◽

Ergodic Theorem ◽

Binary Tree ◽

Generalized Entropy

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The Generalized Entropy Ergodic Theorem for Nonhomogeneous Markov Chains

Journal of Theoretical Probability ◽

10.1007/s10959-015-0597-9 ◽

2015 ◽

Vol 29 (3) ◽

pp. 761-775 ◽

Author(s):

Zhongzhi Wang ◽

Weiguo Yang

Keyword(s):

Markov Chains ◽

Ergodic Theorem ◽

Generalized Entropy ◽

Nonhomogeneous Markov Chains

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The Strong Law of Large Numbers and the Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree

IEEE Transactions on Information Theory ◽

10.1109/tit.2015.2404310 ◽

2015 ◽

Vol 61 (4) ◽

pp. 1640-1648 ◽

Author(s):

Hui Dang ◽

Weiguo Yang ◽

Zhiyan Shi

Keyword(s):

Markov Chains ◽

Ergodic Theorem ◽

Binary Tree ◽

Law Of Large Numbers ◽

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A class of strong deviation theorems for the random fields associated with bifurcating Markov chains indexed by a binary tree

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2019.1648830 ◽

2019 ◽

pp. 1-18 ◽

Author(s):

Pingping Zhong ◽

Zhiyan Shi ◽

Weiguo Yang ◽

Fan Min

Keyword(s):

Markov Chains ◽

Random Fields ◽

Binary Tree ◽

Strong Deviation

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An ergodic theorem for Markov chains

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete ◽

10.1007/bf01844420 ◽

1962 ◽

Vol 1 (2) ◽

pp. 174-176 ◽

Author(s):

Steven Orey

Keyword(s):

Markov Chains ◽

Ergodic Theorem

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Markov approximation and the generalized entropy ergodic theorem for non-null stationary process

Proceedings - Mathematical Sciences ◽

10.1007/s12044-019-0542-4 ◽

2020 ◽

Vol 130 (1) ◽

Author(s):

Zhongzhi Wang ◽

Weiguo Yang

Keyword(s):

Ergodic Theorem ◽

Stationary Process ◽

Markov Approximation ◽

Generalized Entropy

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On the Relation between Limit Theorems of Finite Groups and an Ergodic Theorem for Markov Chains with Doubly Stochastic Transition Matrices

Theory of Probability and Its Applications ◽

10.1137/1110060 ◽

1965 ◽

Vol 10 (3) ◽

pp. 493-496 ◽

Author(s):

V. M. Maksimov

Keyword(s):

Markov Chains ◽

Ergodic Theorem ◽

Finite Groups ◽

Limit Theorems ◽

Transition Matrices ◽

Doubly Stochastic ◽

Stochastic Transition

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Computation and Estimation of Generalized Entropy Rates for Denumerable Markov Chains

IEEE Transactions on Information Theory ◽

10.1109/tit.2011.2133710 ◽

2011 ◽

Vol 57 (7) ◽

pp. 4026-4034 ◽

Author(s):

Gabriela Ciuperca ◽

Valerie Girardin ◽

Loïck Lhote

Keyword(s):

Markov Chains ◽

Generalized Entropy

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Equivalent properties for the bifurcating Markov chains indexed by a binary tree

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2020.1742923 ◽

2020 ◽

pp. 1-9

Author(s):

Zhiyan Shi ◽

Weiguo Yang ◽

Ying Tang

Keyword(s):

Markov Chains ◽

Binary Tree ◽

Equivalent Properties

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Different Closed-Form Expressions for Generalized Entropy Rates of Markov Chains

Methodology And Computing In Applied Probability ◽

10.1007/s11009-018-9679-3 ◽

2018 ◽

Vol 21 (4) ◽

pp. 1431-1452

Author(s):

Valérie Girardin ◽

Loick Lhote ◽

Philippe Regnault

Keyword(s):

Markov Chains ◽

Closed Form ◽

Generalized Entropy

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An Alternative Method of the Proof of the Ergodic Theorem for General Markov Chains

Theory of Probability and Its Applications ◽

10.1137/s0040585x97t990459 ◽

2021 ◽

Vol 66 (3) ◽

pp. 364-375

Author(s):

S. V. Nagaev

Keyword(s):

Markov Chains ◽

Ergodic Theorem ◽

Alternative Method

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