摘要
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.通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,研究给出了一类非齐次树上m阶非齐次马氏链的若干强极限定理.
In recent years, tree indexed stochastic process has become one of the research directions for studying in the probability theory. The strong limit theorems has been one of the central issues of the international probability theory. In this paper, through constructing a non-negative martingale and applies Doob＇s martingale convergence theorem to the research of a.e. convergence, a class of strong limit theorems for m-order non-homogeneous Markov chain on a non-homogenous tree are given.
出处
《数学的实践与认识》
北大核心
2016年第2期234-240,共7页
Mathematics in Practice and Theory
基金
河北省高等学校科学技术研究重点项目(ZD2014051)
关键词
非齐次树
鞅
马氏链
强极限定理
non-homogeneous tree
martingale
Markov chain
strong limit theorem
