Transient analysis of immigration birth-death processes with total catastrophes

Xiuli Chao, Yuxi Zheng

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

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
Volume17
Issue number1
DOIs
StatePublished - Jan 1 2003

Fingerprint

Birth-death Process
Transient Analysis
Immigration
Catastrophe
Transient analysis
Closed-form
Partial differential equation
Transient Solution
Partial differential equations
Method of Characteristics
Equilibrium Distribution
Closed-form Solution
Stochastic Systems
Ordinary differential equation
Probability Distribution
Stochastic systems
Ordinary differential equations
Probability distributions
Closed-form solution
Equilibrium distribution

All Science Journal Classification (ASJC) codes

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

Cite this

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Transient analysis of immigration birth-death processes with total catastrophes. / Chao, Xiuli; Zheng, Yuxi.

In: Probability in the Engineering and Informational Sciences, Vol. 17, No. 1, 01.01.2003, p. 83-106.

Research output: Contribution to journalArticle

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