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Branching processes in a random environment with immigration stopped at zero

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  04 May 2020

Elena Dyakonova ,
Doudou Li ,
Vladimir Vatutin  and
Mei Zhang
Elena Dyakonova*
Affiliation:
Steklov Mathematical Institute
Doudou Li*
Affiliation:
Beijing Normal University
Vladimir Vatutin*
Affiliation:
Steklov Mathematical Institute and Beijing Normal University
Mei Zhang*
Affiliation:
Beijing Normal University
*
*Postal address: Steklov Mathematical Institute, 8 Gubkin St., Moscow, 119991, Russia.
***Postal address: School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, P.R. China.
*Postal address: Steklov Mathematical Institute, 8 Gubkin St., Moscow, 119991, Russia.
**Email address: elena@mi-ras.ru
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Abstract

A 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.

Keywords

Branching processrandom environmentimmigrationlife period

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 1 , March 2020 , pp. 237 - 249
Copyright
© Applied Probability Trust 2020

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