Abstract.In this paper, we study the strong limit theorems on the a.s. convergence for the harmonic mean of the transition probabilities of nonhomogeneous Markov chain indexed by the generalized Bethe tree on the generalized random selection system. In the proof, we apply the tool of conditional moment generating functions and the consistent distribution functions to the study of strong limit theorems for Markov chains indexed by the generalized Bethe tree. As corollaries, some strong limit theorems for the Markov chains field on the generalized Bethe and the nonhomogeneous Markov chain are obtained. Some results which have been obtained are extended.

Received: September 27, 2009

AMS Subject Classification: 60F15

Key Words and Phrases: nonhomogeneous Markov chains field, the generalized Bethe tree, harmonic mean, the conditional moment generating function, transition probability

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 2