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

Chunmao Huang and Quansheng Liu

Stochastic Processes and their Applications, 2012, vol. 122, issue 2, 522-545

Abstract: 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.

Keywords: Branching process; Random environment; Moments; Harmonic moments; Large deviation; Moderate deviation; Central limit theorem (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (12)

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DOI: 10.1016/j.spa.2011.09.001

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