In this paper, we study the strong law of large numbers on the frequencies of states for a Markov chains field on a Bethe tree. In the proof, we apply a new technique in the study of the strong limit theorem.

Let {Xn, n[greater-or-equal, slanted]0} be a sequence of random variables on the probability space ([Omega],F,P) taking values in the alphabet S={1,2,...,N}, and Q be another probability measure on F, under which {Xn, n[greater-or-equal, slanted]0} is a Markov chain. Let h(P Q) be the sample...

In this paper, the strong limit theorems for arbitrary stochastic sequences are studied. Some convergence theorems for martingale difference sequence and a class of strong limit theorem for countable nonhomogeneous Markov chains are the particular cases of the results of this paper. Finally, the...