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A class of strong limit theorems for inhomogeneous Markov chains indexed by a generalized Bethe tree on a generalized random selection system

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Ukrainian Mathematical Journal Aims and scope

We study strong limit theorems for a sequence of bivariate functions for an inhomogeneous Markov chain indexed by a generalized Bethe tree on a generalized random selection system by constructing a nonnegative martingale. As corollaries, we generalize results of Yang and Ye and obtain some limit theorems for frequencies of states, ordered couples of states, and the conditional expectation of a bivariate function on a Cayley tree.

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Authors and Affiliations

  1. School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang, China

    Kangkang Wang

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  1. Kangkang Wang
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 10, pp. 1336–1351, October, 2011.

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Wang, K. A class of strong limit theorems for inhomogeneous Markov chains indexed by a generalized Bethe tree on a generalized random selection system. Ukr Math J 63, 1517–1533 (2012). https://doi.org/10.1007/s11253-012-0597-1

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  • DOI: https://doi.org/10.1007/s11253-012-0597-1

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