Berry–Esseen’s bound and Cramér’s large deviation expansion for a supercritical branching process in a random environment

Ion Grama, Quansheng Liu and Eric Miqueu

Stochastic Processes and their Applications, 2017, vol. 127, issue 4, 1255-1281

Abstract: Let (Zn) be a supercritical branching process in a random environment ξ=(ξn). We establish a Berry–Esseen bound and a Cramér’s type large deviation expansion for logZn under the annealed law P. We also improve some earlier results about the harmonic moments of the limit variable W=limn→∞Wn, where Wn=Zn/EξZn is the normalized population size.

Keywords: Branching processes; Random environment; Harmonic moments; Stein’s method; Berry–Esseen bound; Change of measure (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2016.07.014

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