求齐次有限马尔科夫链状态空间全体闭集的算法

Algorthms for Computing the Family of Closed Sets of State Space of a Homogeneous Fintite Markov Chain

本文给出了齐次有限马尔科夫链状态空间的闭集族的算法，为了减少计算量和无重复地列出全体闭集，引进了状态空间压缩法和逐点删去法。对状态个数不太大的情形，可利用压缩状态空间的状态转移图求全体闭集；对一般情形，给出了计算机算法。

In this paper. some algorithms for computing the family of closed sets of state space of a homogeneous finite Markov chain are presented. In order to reduce the computation and list all of closed sets without repetition, the method of compression of state space and the method of elimination point by point are introduced here. When the number of states is moderate, we can obtain immediately the family of closed sets by means of the compression directed graph of state space.