Integro-local limit theorems for supercritical branching process in a random environment Full article
| Journal |
Statistics and Probability Letters
ISSN: 0167-7152 |
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| Output data | Year: 2022, Volume: 181, Article number : 109234, Pages count : DOI: 10.1016/j.spl.2021.109234 | ||
| Tags | Branching process; Large deviations; Light tail distribution; Random environment | ||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Russian Foundation for Basic Research | 20-51-12007 |
| 2 | Sobolev Institute of Mathematics | 0250-2019-0001 |
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.
Cite:
Struleva M.A.
, Prokopenko E.I.
Integro-local limit theorems for supercritical branching process in a random environment
Statistics and Probability Letters. 2022. V.181. 109234 . DOI: 10.1016/j.spl.2021.109234 WOS Scopus РИНЦ OpenAlex
Integro-local limit theorems for supercritical branching process in a random environment
Statistics and Probability Letters. 2022. V.181. 109234 . DOI: 10.1016/j.spl.2021.109234 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000712136100008 |
| Scopus: | 2-s2.0-85116937781 |
| Elibrary: | 47512243 |
| OpenAlex: | W3204686564 |