Markov链的一种随机时间替换

研究Markov链的一种随机时间替换,这种替换有别于通常的Markov过程理论中的随机时间替换。通常的Markov过程的随机时间替换,是通过Markov过程的可加泛函来实现的。而现在,被随机时间替换的过程X={X(n),n=0,1,2…}是一个时间离散的、状态空间可数的、时间齐次的Markov链,用于随机时间替换的过程ι={ιt,t≥0}是一个时间连续的、状态空间为非负整数集的、不降的、空间齐次的Markov链,而且X与独立。证明了随机时间替换后的过程,Y={Y(t),t≥0},Y(t)=X(ιt)是一个Markov链;并求出了Y的转移概率;当是时间齐次时,Y也是时间齐次的。

A Sort of Random Time-Change for Markov Chain Mo Xiaoyun

Researches a sort of random time-change for a Markov chain, which is different from random time-change of ordinary Markov process theory. It is realized by additive functional of the Markov process. The process which will be random time-substituted is a time-discrete, countable state space and time-homogeneous Markov chain, and the process which will be used to substitute is a time-continuous, non-decreasing and space-homogeneous Markov chain with the state-space constituting of non-negative integers, X and are mutually independent. It is proved that the random time-changed process , is a Markov chain, whose transition probabilities are calculated. If is time-homogeneous, then Y is also time-homogeneous.