关于渐近循环马氏链的强大数定律

Strong law of large numbers for asymptotic circular Markov chains

研究了一类非齐次马氏链———渐近循环马氏链的强大数定律.首先引出了渐近循环马氏链的概念,然后给出了一些引理;利用了信源的二元函数平均的一个极限定理,该定理是利用鞅差序列的收敛定理得到的;最后利用了渐近循环马氏链关于状态序偶出现频率的强大数定理给出并证明了关于渐近循环马氏链的强大数定律,该定理作为推论可以得到已有的结果.

In this paper,the strong law of large numbers for asymptotic circular Markov chains in nonhomogenous Markov chains was studied.The definition of asymptotic circular Markov chains was introduced.The limit theorem for the average of the two functions was applied,which was obtained from the convergence theorem for martingale difference sequence.By the strong law of large numbers for asympto-tic circular Markov chains on the frequencies of occurrence of states,the strong law of large numbers for asymptotic circular Markov chains in nonhomogenous Markov chains was deduced and proved.Some known results can be generalized by the proposed law.