Subcritical branching processes in a random environment without the Cramer condition

Vladimir Vatutin and Xinghua Zheng

Stochastic Processes and their Applications, 2012, vol. 122, issue 7, 2594-2609

Abstract: A subcritical branching process in random environment (BPRE) is considered whose associated random walk does not satisfy the Cramer condition. The asymptotics for the survival probability of the process is investigated, and a Yaglom type conditional limit theorem is proved for the number of particles up to moment n given survival to this moment. Contrary to other types of subcritical BPRE, the limiting distribution is not discrete. We also show that the process survives for a long time owing to a single big jump of the associate random walk accompanied by a population explosion at the beginning of the process.

Keywords: Branching process; Random environment; Random walk; Survival probability; Functional limit theorem (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2012.04.008

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