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LINEAR BIRTH/IMMIGRATION-DEATH PROCESS WITH BINOMIAL CATASTROPHES

Published online by Cambridge University Press:  14 October 2015

Stella Kapodistria ,
Tuan Phung-Duc  and
Jacques Resing
Stella Kapodistria
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands E-mail: [email protected]
Tuan Phung-Duc
Affiliation:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan E-mail: [email protected]
Jacques Resing
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands E-mail: [email protected]
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 1 , January 2016 , pp. 79 - 111
Copyright
Copyright © Cambridge University Press 2015 

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