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Article Dans Une Revue Stoch. proc. appl. Année : 2012

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

Résumé

Let $(Z_{n})$ be a supercritical branching process in a random environment $\xi $, and $W$ be the limit of the normalized population size $Z_{n}/\mathbb{E}[Z_{n}|\xi ]$. We show large and moderate deviation principles for the sequence $\log Z_{n}$ (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 $Z_{n}$. Central limit theorems on $W-W_n$ and $\log Z_n$ are also established.

Dates et versions

hal-00909160 , version 1 (25-11-2013)

Identifiants

Citer

Chunmao Huang, Quansheng Liu. Moments, moderate and large deviations for a branching process in a random environment. Stoch. proc. appl., 2012, 122, pp.522-545. ⟨10.1016/j.spa.2011.09.001⟩. ⟨hal-00909160⟩
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