Author:
Kapodistria Stella,Phung-Duc Tuan,Resing Jacques
Abstract
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.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
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