Moments, moderate and large deviations for a branching process in a random environment

Let (Zn) be a supercritical branching process in a random environment ξ, and W be the limit of the normalized population size Zn/E[Zn|ξ]. We show large and moderate deviation principles for the sequence logZn (with appropriate normalization). For the proof, we calculate the critical value for the existence of harmonic moments of W, and show an equivalence for all the moments of Zn. Central limit theorems on W−Wn and logZn are also established.

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Year of publication:	2012
Authors:	Huang, Chunmao ; Liu, Quansheng
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 122.2012, 2, p. 522-545
Publisher:	Elsevier
Subject:	Branching process \| Random environment \| Moments \| Harmonic moments \| Large deviation \| Moderate deviation \| Central limit theorem

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011064888