Subcritical Branching Processes in Random Environment with Immigration Stopped at Zero

Doudou Li (), Vladimir Vatutin () and Mei Zhang ()
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Doudou Li: Beijing Normal University
Vladimir Vatutin: Steklov Mathematical Institute
Mei Zhang: Beijing Normal University

Journal of Theoretical Probability, 2021, vol. 34, issue 2, 874-896

Abstract: Abstract We consider the subcritical branching processes with immigration which evolve under the influence of a random environment and study the tail distribution of life periods of such processes defined as the length of the time interval between the moment when first invader (or invaders) came to an empty site until the moment when the site becomes empty again. We prove that the tail distribution decays with exponential rate. The main tools are change of measure and some conditional limit theorems for random walks.

Keywords: Branching processes; Random environment; Immigration; Life period; 60J80; 60F99 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-00991-5

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