不可约闭集的余集为有限集的Markov链的吸收概率(英文)

ABSORPTION PROBABILITIES OF MARKOV CHAINS HAVING A FINITE COMPLEMENT OF IRREDUCIBLE CLOSED SETS

一个Markov链的状态空间Ψ可以分解为一系列互不相交的不可约闭集C1,…,Ck,…,及其余集ΨT。对于ΨT为一个非空有限集的情形,给出了用于计算吸收概率的一些公式,证明了关于首达时的一些很直观的性质。

The state space Ψ of a Markov chain Xn, n≥0,is decomposed into disjoint irreducible closed sets C1, C2, ..., Ck, ..., and their complement ΨT. In case ΨT is nonempty and finite, several formulas in terms of the transition function matrix for computing the absorption probabilities have been found, and some intuitive properties about the hitting time have also been proved.