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Multitype processes with reproduction-dependent immigration

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Ibrahim Rahimov
Ibrahim Rahimov*
Affiliation:
University of Science Malaysia
*
∗Postal address: (i) School of Mathematical Sciences, University of Science Malaysia, 11800, Penang, Malaysia; (ii) Institute of Mathematics, Hodjaev St., 29, 700143, Tashkent, Uzbekistan. E-mail address: rahimov@dpc.kfupm.edu.sa
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Abstract

The multitype discrete time indecomposable branching process with immigration is considered. Using a martingale approach a limit theorem is proved for such processes when the totality of immigrating individuals at a given time depends on evolution of the processes generating by previously immigrated individuals. Corollaries of the limit theorem are obtained for the cases of finite and infinite second moments of offspring distribution in critical processes.

Keywords

Multitypeindecomposablecriticalityimmigrationdependencestopping time

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G70: Extreme value theory; extremal processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 281 - 292
Copyright
Copyright © Applied Probability Trust 1998 

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