The generalized entropy ergodic theorem for Markov chains indexed by a spherically symmetric tree

Zhiyan Shi, Xinyue Xi and Qingpei Zang

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 6, 2178-2193

Abstract: In information theory, the entropy ergodic theorem is a fundamental one well-known to all. In this article, we will study the generalized entropy ergodic theorem for Markov chains indexed by a spherically symmetric tree. First, we give the definition of Markov chains indexed by a spherically symmetric tree. Meanwhile, the generalized strong law of large numbers for Markov chains indexed by a spherically symmetric tree is proved. Finally, we obtain the generalized entropy ergodic theorem for Markov chains indexed by a spherically symmetric tree.

Date: 2024
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DOI: 10.1080/03610926.2022.2122839

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