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Death and Birth-Death and Immigration Processes with Catastrophes

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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.

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Correspondence to J. Gani.

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Gani, J., Swift, R.J. Death and Birth-Death and Immigration Processes with Catastrophes. J Stat Theory Pract 1, 39–48 (2007). https://doi.org/10.1080/15598608.2007.10411823

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  • DOI: https://doi.org/10.1080/15598608.2007.10411823

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