Transient analysis of immigration birth-death processes with total catastrophes. (English) Zbl 1019.60079
Very few stochastic systems are known to have closed-form transient solutions. The authors consider an immigration birth-death population process with total catastrophes and study its transient as well as equilibrium behavior. They obtain closed-form solutions for the equilibrium distribution as well as the closed-form transient probability distribution at any time. The approach involves solving ordinary differential equations, and the method of characteristics is used in solving partial differential equations.
Reviewer: Zhenghu Li (Beijing)
MSC:
60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |