Branching processes in a random environment with immigration stopped at zero

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2020Embargo end date: 01 Jan 2019 English Publisher:Cambridge University Press (CUP)Journal:Journal of Applied Probability, volume 57, pages 237-249 (issn: 0021-9002, eissn: 1475-6072,

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Authors: Elena Dyakonova; Doudou Li; Vladimir Vatutin; Mei Zhang;

doi: 10.1017/jpr.2019.94 , 10.48550/arxiv.1905.03535

arXiv: 1905.03535

Branching processes in a random environment with immigration stopped at zero

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Abstract

AbstractA critical branching process with immigration which evolves in a random environment is considered. Assuming that immigration is not allowed when there are no individuals in the population, we investigate the tail distribution of the so-called life period of the process, i.e. the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time.

Related Organizations

Department of Mathematical Sciences
Russian Federation
Steklov Mathematical Institute
Russian Federation
Beijing Normal University
China (People's Republic of)

Keywords

random environment, Branching processes (Galton-Watson, birth-and-death, etc.), Probability (math.PR), FOS: Mathematics, life period, 60J80, 60F99, Mathematics - Probability, branching process, immigration

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