TRANSIENT ANALYSIS OF IMMIGRATION BIRTH–DEATH PROCESSES WITH TOTAL CATASTROPHES

Authors:
Xiuli Chao;Yuxi Zheng
Affiliations:
Department of Industrial Engineering, North Carolina State University, Raleigh, NC 27695-7906, E-mail: xchao@unity.ncsu.edu;Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, E-mail: yzheng@math.psu.edu
Venue:
Probability in the Engineering and Informational Sciences
Year:
2003

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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.