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
Death Process Birth-Death and Immigration Process Catastrophes Probability Generating Functions (pgfs) Poisson Process Stationary Distributions
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Economou, A., Fakinos, D., 2003. A continuous time Markov chain under the influence of a regulating point process and applications in stochastic models with catastrophes. Europ. J. Operat. Res. 149, 625–640.MathSciNetCrossRefGoogle Scholar