Markov过程的一个不变测度问题

A Problem about Invariant Measure in Markov Processes

马尔可夫链的不变测度在马尔可夫过程的常返性和遍历性的研究中具有十分重要的地位。该文利用了不中断分解定理得到了遍历 Q过程R(λ)的不变测度和一类单瞬时态拟 Q -矩阵的不变测度的一般表达形式 ,并构造了一个Kolmogorov矩阵 ,解决了在单瞬时态不可和的条件下D .Williams教授提出的开问题 ,即给定已知不变测度的条件 ,Q过程的存在性问题。

In researching recurrent Qprocess and ergodic Qprocess for Markov processes, studying the invariant measure is very important for Markov chains. In this paper, utilizing the uninterrupt decomposition theorem, we obtain the general formulation of the invariant measure for ergodic Qprocess, and obtain the general formulation of invariant measure about a class of quasi Q-matrix with single instantaneous state. Based on the results, we construct a Kolomogorov matrix and solve the open problem proposed by professor D.Williams, namely,the existence of Qprocess with a given invariant measure.