Integro-local limit theorems for supercritical branching process in a random environment

M.A. Struleva and E.I. Prokopenko

Statistics & Probability Letters, 2022, vol. 181, issue C

Abstract: Let Zn be a supercritical branching process in a random environment (BPRE). Under certain moment assumptions, we present the precise asymptotics for the “integro-local” probabilities P(logZn∈[x(n),x(n)+Δn)), where Δn→0 and x(n)→∞ as n→∞. In particular, this implies the large deviations tail asymptotics for P(logZn⩾x(n)) as n→∞. Like in previous research, we can see that, in the light-tail case, the main term in the large deviations asymptotics for the BPRE is provided by the associated random walk.

Keywords: Large deviations; Branching process; Random environment; Light tail distribution (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109234

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