广义赌博系统m阶非齐次马氏链强极限定理的研究

Strong limit theorem of m-order nonhomogeneous Markov chains on fair gambling system

运用条件概率的概念,采用鞅方法将Bernoulli序列赌博系统的强极限定理推广到m阶非齐次马氏链的情况.研究得到了对赌博系统中m阶非齐次马氏链普遍成立的一类强极限定理.并通过允许选择函数在任意实数集上取值,对选择函数的概念进行推广.作为推论得到了一系列赌博系统的强极限定理.

Based on the notion of conditional probability and martingale method,strong limit theorems on gambling system for Bernoulli sequences were extended to m-order nonhomogeneous Markov chains in this paper.Moreover,the conception of random selection was generalized by allowing the selection function to take values in an interval.As corollaries,a class of strong large number theorems on gambling system was obtained.