非齐次树上连续状态马氏链广义赌博系统的强极限定理

Some strong limit theorems on the generalized gambling system for Markov chains of continuous state space on a non-homogeneous tree

树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强极限定理一直是国际概率论界研究的中心课题之一.本文通过构造元乘积密度函数与适当的非负鞅,利用Doob鞅收敛定理给出了一类特殊非齐次树上连续状态马氏链广义赌博系统的强极限定理.

In recent years, tree indexed stochastic process has become one of the research directions in the study of the probability theory. The strong limit theorem has been one of the central issues of the international probability theory. In this paper, by constructing n-element product density functions and a non-negative martingale and applying Doob＇s martingale convergence theorem, we give some strong limit theorems on the generalized gambling system for Markov chains of continuous state space on a special non-homogeneous tree.