非时齐马尔科夫链及其轨道的概率构造

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.

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

In this paper,we present a probabilistic 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.