Large deviations for sums associated with supercritical branching process in a random environment

Yinxuan Zhao and Mei Zhang

Statistics & Probability Letters, 2024, vol. 207, issue C

Abstract: In this paper, we study the random sum SZn of independent and identically distributed (i.i.d.) random variables {Xi}, where {Zn} is a supercritical branching process in an i.i.d. environment ξ, and X1 is of zero mean and finite variance. We shall prove the large deviations of SZn, first in the case that Z1 has linear fractional distribution, then in some general case.

Keywords: Branching process; Random environment; Large deviation; Supercritical; Linear fractional (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2023.110019

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