生灭过程的平稳性与拟平稳性

Stationarity and quasi-stationarity for birth-death processes

王梓坤先生对生灭过程的构造性理论做出了开创性工作,这些工作产生了深远的影响.本文将阐述4种无穷边界的生灭过程的平稳性和拟平稳分布的存在唯一性.特别地,本文证明了具有流出边界和正则边界的最小生灭过程的拟平稳分布的存在唯一性.这些结果得益于王梓坤先生和杨向群教授关于生灭过程的构造论.最后,本文提出生灭过程的拟平稳分布的一些待解决问题.

Professor Zikun Wang has made pioneering research on the construction theory of birth-death processes,which now has many applications.We review the quasi-stationary distribution for birth-death processes with four types of infinity boundary.In the cases of exit/regular boundaries,we extend the quasi-stationary distributions to the minimal processes,which have finite explosion time.The arguments depend heavily on the construction theory by Professors Zikun Wang and Xiang-Qun Yang.Some open problems are presented for the quasi-stationary distributions of birth-death processes.