Linear birth/immigration-death process with binomial catastrophes

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In this paper, we study birth/immigration-death processes under mild (binomial) catastrophes. We obtain explicit expressions for both the time-dependent (transient) and the limiting (equilibrium) factorial moments, which are then used to construct the transient and equilibrium distribution of the population size. We demonstrate that our approach is also applicable to multidimensional systems such as stochastic processes operating under a random environment and other variations of the model at hand. We also obtain various stochastic order results for the number of individuals with respect to the system parameters, as well as the relaxation time. Keywords: birth-death processes; catastrophes; time-dependent and equilibrium moments; equilibrium distribution; relaxation time
Originele taal-2Engels
Pagina's (van-tot)79-111
TijdschriftProbability in the Engineering and Informational Sciences
Volume30
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - jan 2016

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