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TRANSIENT ANALYSIS OF IMMIGRATION BIRTH–DEATH PROCESSES WITH TOTAL CATASTROPHES

Published online by Cambridge University Press:  07 January 2003

Xiuli Chao  and
Yuxi Zheng
Xiuli Chao
Affiliation:
Department of Industrial Engineering, North Carolina State University, Raleigh, NC 27695-7906, E-mail: xchao@unity.ncsu.edu
Yuxi Zheng
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, E-mail: yzheng@math.psu.edu
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Abstract

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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 17 , Issue 1 , January 2003 , pp. 83 - 106
Copyright
© 2003 Cambridge University Press