Branching processes in random environment with immigration stopped at zero

Elena Dyakonova; Doudou Li; Vladimir Vatutin; Mei Zhang

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arXiv · 1905.03535

Branching processes in random environment with immigration stopped at zero

Elena Dyakonova·Doudou Li·Vladimir Vatutin·Mei Zhang

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Abstract

A critical branching process with immigration which evolve in a random environment is considered. Assuming that immigration is not allowed when there are no individuals in the aboriginal 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.

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Elena Dyakonova, Doudou Li, Vladimir Vatutin, Mei Zhang. 2019-05-09. Branching processes in random environment with immigration stopped at zero. https://arxiv.org/abs/1905.03535

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