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Asymptotic local lower deviations of strictly supercritical branching process in a random environment with geometric distributions of descendants.

Authors :
Denisov, K. Yu.
Source :
Discrete Mathematics & Applications. Aug2024, Vol. 34 Issue 4, p197-206. 10p.
Publication Year :
2024

Abstract

We consider local probabilities of lower deviations for branching process Zn = Xn,1 + ⋯ + Xn,Zn−1 in random environment η. We assume that η is a sequence of independent identically distributed variables and for fixed η the variables Xi,j are independent and have geometric distributions. We suppose that steps ξi of the associated random walk Sn = ξ1 + ⋯ + ξn has positive mean and satisfies left-side Cramér condition: E exp(hξi) < ∞ if h− < h < 0 for some h− < − 1. Under these assumptions we find the asymptotic of the local probabilities P(Zn = ⌊exp(θn)⌋), n → ∞, for θ ∈ (max(m−, 0); m(− 1)) and for θ in a neighbourhood of m(− 1), where m− and m(− 1) are some constants. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
09249265
Volume :
34
Issue :
4
Database :
Academic Search Index
Journal :
Discrete Mathematics & Applications
Publication Type :
Academic Journal
Accession number :
178947031
Full Text :
https://doi.org/10.1515/dma-2024-0016