可列非齐次马氏链泛函的一类强大数定律

A CLASS OF STRONG LAWS OF LARGE NUMBERS FOR FUNCTIONALS OF COUNTABLE NONHOMOGENEOUS MARKOV CHAINS

本文用分析方法研究可列非齐次马氏链的泛函的极限性质，得到了一类不同形式的强大数定律，在其中通常形式的强大数定律中的数学期望被条件期望所代替，关于独立随机变量序列的若干经典强大数定律是本文结果的推论．

In this paper the limit properties of the functionals {fn(Xn) } of a countable nonhomogeneous Markov chain {Xn} are studied by using an analytic approach, and a class of strong laws of large numbers with different form from the usual ones are obtained, where the conditional expectation is used instead of the expectation in the usual form of the strong law of large numbers. Some classical results on strong law of large numbers for the independent random sequences are corollaries of the results of this paper.