关于非齐次树指标马氏链随机矩阵的一个强偏差定理

A strong deviation theorem for the transition matrix of Markov chains indexed by 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。在概率论的发展过程中,对强偏差定理的研究一直占重要地位,强偏差定理也一直是国际概率论界研究的中心课题之一。本文通过引入滑动相对熵的概念和构造非负鞅,利用Doob鞅收敛定理给出了关于非齐次树指标马氏链的状态出现次数与随机转移概率之间的一个强偏差定理。

Stochastic process indexed by a tree has become a hot topic in the field of the probability theory in recent years.The researh of the strong deviation theorem has held an important position in the development of probability theory,and the strong deviation theorem is one of the central issues of the international probability theory.In this paper,by introducing the concept of moving relative entropy and constructing non-negative martingale,a strong deviation theorem of the relationship between the number of occurrences of state and the random transition probability for Markov chains indexed by a non-homogeneous tree is established by applying martingale convergence theorem.