关于有限非齐次马氏链状态序偶频率的一个强大数定律

A Strong Law of Large Numbers on the Frequency of orderedState Couples for the Finite Nonhomogeneous Markov Chains

设{X_n,n≥0}是以S={1,2,…,m}为状态空间的非齐次马氏链,i,j(?)S,S_n(i,j,w)是序偶列(X_0,X_1),(X_1,X_2),…,(X_(n-1),X_n)中序偶(i,j)出现的次数,本文利用绝对平均收敛的概念给出关于S_n(i,j,w)/n的一个强大数定律。

Let{X_n, n≥0}be a nonhomogeneous Markov chain with the state space S= {1, 2, …, m}, i, j∈S, and S_n(i, j, ω)be the numbers of occurrence of the ordered couples(i, j)among the sequence of the ordered couples(X_0, X_1), (X_1, X_2), …, (X_(n-1), X_n). In this paper a strong law of large numbers for S_n(i, j, ω)/n is obtained by using the notion of absolute convergence on the average,