BERRY-ESSEEN'S BOUND AND CRAMÉR'S LARGE DEVIATION EXPANSION FOR A SUPERCRITICAL BRANCHING PROCESS IN A RANDOM ENVIRONMENT - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Stochastic Processes and their Applications Année : 2017

BERRY-ESSEEN'S BOUND AND CRAMÉR'S LARGE DEVIATION EXPANSION FOR A SUPERCRITICAL BRANCHING PROCESS IN A RANDOM ENVIRONMENT

Résumé

Let (Z n) be a supercritical branching process in a random environment ξ = (ξ n). We establish a Berry-Esseen bound and a Cramér's type large deviation expansion for log Z n under the annealed law P. We also improve some earlier results about the harmonic moments of the limit variable W = lim n→∞ W n , where W n = Z n /E ξ Z n is the normalized population size.
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Dates et versions

hal-01270162 , version 1 (05-02-2016)

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Ion Grama, Quansheng Liu, Eric Miqueu. BERRY-ESSEEN'S BOUND AND CRAMÉR'S LARGE DEVIATION EXPANSION FOR A SUPERCRITICAL BRANCHING PROCESS IN A RANDOM ENVIRONMENT. Stochastic Processes and their Applications, 2017, 127, pp.1255-1281. ⟨10.1016/j.spa.2016.07.014⟩. ⟨hal-01270162⟩
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