渐近循环二阶马氏链的强大数定律

Strong law of large numbers for asymptotic circular second order Markov chains

研究了一类特殊的非齐次马氏链——渐近循环二阶马氏链的强极限定理.首先引进了渐近循环二阶马氏链的概念,然后利用非齐次马氏链三元函数的极限性质,得到了渐近循环二阶马氏链关于状态出现频率的强极限定理,最后得到渐近循环二阶马氏链关于状态出现频率的强大数定律.作为推论推广了二阶非齐次马氏链的强大数定律.渐近循环二阶马氏链的强大数定律可用于信源编码理论.

The strong limit theorem of special nonhomogeneous Markov chains-asymptotic circular second order Markov chains was studied. Firstly, the definition of asymptotic circular second order Markov chains was introduced. Then according to the limit property of nonhomogeneous Markov chains ternary functions, the strong limit theorem of asymptotic circular second order Markov chains for states occurrence frequencies was established. Finally, the strong large numbers law of asymptotic circular second order Markov chains for states occurrence frequencies was obtained. The strong law of large numbers for second order nonhomogeneous Markov chains was extended as a corollary. The strong large numbers law for asymptotic circular second order Markov chains can be used for the source coding theory.