遍历马氏链的常返性

The Recurrence of Ergodic Markov Chains

本文指出遍历马氏链的尾σ-域是平凡的,而且当 n 趋于无穷时P(x_n=j|x_k=i)的极限π_j 大于零是 P(x_n=j,i.o.)=1的充分条件.

In this paper,it is pointed out that the tail σ-field of a ergodic Markov chain must be trivial,and it is a sufficient condition for P(x_n= j,i.o.)=1 that π_j,the limit of P(x_n=j|x_k=i),is greater than zero as n approaches to infinity.