Abstract
Let \((\xi _n)_{n=0}^\infty \) be a nonhomogeneous Markov chain taking values in a finite state-space \(\mathbf {X}=\{1,2,\ldots ,b\}\). In this paper, we will study the generalized entropy ergodic theorem with almost-everywhere and \(\mathcal {L}_1\) convergence for nonhomogeneous Markov chains; this generalizes the corresponding classical results for Markov chains.
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Acknowledgments
The authors are very thankful to Professor Keyue Ding who helped us to improve the English of this paper greatly, and very thankful to the reviewers for their valuable comments.
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This work was supported by the National Natural Science Foundation of China (11071104), the National Natural Science Foundation of Anhui Province (1408085MA04) and Foundation of Anhui Educational Committee (KJ2012B117).
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Wang, Z., Yang, W. The Generalized Entropy Ergodic Theorem for Nonhomogeneous Markov Chains. J Theor Probab 29, 761–775 (2016). https://doi.org/10.1007/s10959-015-0597-9
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DOI: https://doi.org/10.1007/s10959-015-0597-9