Conditional entropy,entropy density,and strong law of large numbers for generalized controlled tree-indexed Markov chains |
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Authors: | Weicai Peng |
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Affiliation: | 1. School of International Business Administration, Shanghai University of Finance and Economics, Shanghai, China;2. Department of Mathematics, Chaohu University, Anhui, China |
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Abstract: | In this paper, we first introduces a tree model without degree boundedness restriction namely generalized controlled tree T, which is an extension of some known tree models, such as homogeneous tree model, uniformly bounded degree tree model, controlled tree model, etc. Then some limit properties including strong law of large numbers for generalized controlled tree-indexed non homogeneous Markov chain are obtained. Finally, we establish some entropy density properties, monotonicity of conditional entropy, and entropy properties for generalized controlled tree-indexed Markov chains. |
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Keywords: | AEP conditional entropy controlled tree entropy density strong law of large numbers |
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