2017
Том 69
№ 9

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

Kangkang Wang

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Abstract

We study strong limit theorems for a bivariate function sequence of an nonhomogeneous 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 Cayley tree.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 10, pp 1517-1533.

Citation Example: Kangkang Wang A class of strong limit theorems for nonhomogeneous Markov chains indexed by a generalized Bethe tree on a generalized random selection system // Ukr. Mat. Zh. - 2011. - 63, № 10. - pp. 1336-1351.

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