非时齐马尔科夫链及其轨道的概率构造  

A Probabilistic Construction of Non-homogenous Markov Chain and Its Trojectory

作　　者：王家赠[1] 彭为花 

机构地区：[1]北京工商大学理学院,北京100048

出　　处：《数学的实践与认识》2017年第6期144-152,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11001004)

摘　　要：给出了一种由局部刻画构造非时齐马尔科夫链的概率方法.以任意时刻之后第一次跳的时间为条件,证明了过程的马尔科夫性,同时得到了转移概率的递归表达式—这种做法使其概率意义得以明确呈现,并且进一步证明了强马尔科夫性等一系列性质.这为数值模拟,即以Monte Carlo生成非时齐Q-过程的随机轨道提供了严格的理论基础.In this paper, we present u prob^bilistic method to construct non-homogenous Markov chain with a local characterization. Conditioning on the first jump time after any given time point t, we prove the Markov property of the process, and get the recursive formula of the transition probability. Furthermore, series properties, such as strong Markov property, are proved, the equivalent conditions of the uniqueness are presented. This work provides a rigorous foundation for numerical simulations, i.e, producing the trajectory of non-homogenous Markov chain.

关 键 词：局部刻画 强马尔科夫性 最小解 

分 类 号：O211.62[理学—概率论与数理统计]