任意随机变量序列关于广义随机选择系统的若干极限性质

Some limit properties for the sequence of arbitrary random variables on their generalized random selection system

采用鞅方法研究了对任意随机变量序列关于广义随机选择普遍成立的一类强极限定理,并作为推论得到了m阶马氏过程,鞅序列,鞅差序列,独立随机变量序列的一类强极限定理.把赌博系统的随机变换概念推广到任意随机变量序列,得到了任意随机变量序列随机选择与公平比的若干极限定理.

In this paper, some strong limit theorems for the sequence of arbitrary random variables on generalized random selection are discussed by means of martingale method. As corollaries, a kind of strong large number law for m-order Markov chains, martingale difference sequence and the sequence of independent random variables is obtained. Moreover, the idea of random transformation of gambling system is extended to the sequence of arbitrary random variable, and some limit theorems for their random selection and random equitable ratios are obtained.