Transient analysis of immigration birth-death processes with total catastrophes

Xiuli Chao, Yuxi Zheng

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


Very few stochastic systems are known to have closed-form transient solutions. In this article we consider an immigration birth and death population process with total catastrophes and study its transient as well as equilibrium behavior. We obtain closed-form solutions for the equilibrium distribution as well as the closed-form transient probability distribution at any time t ≥ 0. Our approach involves solving ordinary and partial differential equations, and the method of characteristics is used in solving partial differential equations.

Original languageEnglish (US)
Pages (from-to)83-106
Number of pages24
JournalProbability in the Engineering and Informational Sciences
Issue number1
StatePublished - 2003

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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