中文摘要：

给出了状态有限的单无限马氏环境中马氏链泛函加权和的强收敛性,得到了状态有限的单无限马氏环境中马氏链泛函加权和的强收敛性成立的一系列充分条件.

英文摘要：

This paper studies the strong convergence of the weighted sums of function for finite state Markov chains in single infinitely Markovian environments,and obtains some sufficient conditions for the strong convergence of the weighted sums.