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TRANSIENT ANALYSIS OF IMMIGRATION BIRTH–DEATH PROCESSES WITH TOTAL CATASTROPHES

  • Xiuli Chao (a1) and Yuxi Zheng (a2)

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.

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