Journal of Statistical Theory and Practice

, Volume 1, Issue 1, pp 39–48

# Death and Birth-Death and Immigration Processes with Catastrophes

• J. Gani
• R. J. Swift
Article

## Abstract

This paper explores an alternative approach starting from first principles, to the derivation of probability generating functions (pgfs) of death, birth-death and immigration processes in continuous time, subject to random catastrophes. A more elementary version of the general method proposed by Economou and Fakinos (2003) is presented. We examine the simple death process, the survival of susceptibles in a carrier-borne epidemic, the birth-death and immigration process, the unbiased random walk and the barber shop queue, all of them subject to random catastrophes occurring as a Poisson process. The stationary pgfs and the expected values of the processes are derived.

60J80

## Keywords

Death Process Birth-Death and Immigration Process Catastrophes Probability Generating Functions (pgfs) Poisson Process Stationary Distributions

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