m阶非齐次马氏链关于广义赌博系统的一类强极限定理

A class of strong limit theorems for m-order nonhomogeneous Markov chians on fair gambling system

文中采用条件矩母函数与鞅理论相结合的方法,研究m阶非齐次马氏链关于公平赌博系统的一类强极限定理.通过允许选择函数在一个区间中取值,推广了随机选择的概念.作为推论得到了一般情况下m阶非齐次马氏链的强极限定理以及m元状态序组关于广义随机选择的一类强极限定理.

In this paper, a class of strong limit theorems for m-order nonhomogeneous Markov chains on fair gambling system are discussed by using the conditional generating function and martingale method. Moreover, the conception of random selection is generalized by allowing the selection function to take values in an interval. As corollaries, the strong limit theorem for m-order nonhomogeneous Markov chains on the common condition and a class of strong limit theorems for m-state tuple of the sequence on the generalized random selection are ob- tained.