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Death and Birth-Death and Immigration Processes with Catastrophes

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.

AMS Subject Classification

60J80 

Keywords

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

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References

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Copyright information

© Grace Scientific Publishing 2007

Authors and Affiliations

  1. 1.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia
  2. 2.Department of Mathematics and StatisticsCalifornia State Polytechnic University, PomonaPomonaUSA

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