Comptes Rendus
Probability Theory
Harmonic moments and large deviations for a supercritical branching process in a random environment
[Moments harmoniques et grandes déviations pour un processus de branchement sur-critique dans un environnement aléatoire]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1199-1202.

Soient (Zn) un processus de branchement sur-critique dans un environnement aléatoire ξ, et W la limite de la population normalisée Zn/E[Zn|ξ]. Nous montrons les principes de grande déviation et de déviation modérée pour la suite logZn en trouvant un équivalent des moments de Zn et un critère pour lʼexistence des moments harmoniques de W.

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) by finding an equivalence of the moments of Zn and a criterion for the existence of harmonic moments of W.

Reçu le :
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DOI : 10.1016/j.crma.2011.10.001

Chunmao Huang 1, 2 ; Quansheng Liu 1, 2

1 Université de Bretagne-Sud, LMAM, campus de Tohannic, BP 573, 56017 Vannes, France
2 Université Européenne de Bretagne, France
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Chunmao Huang; Quansheng Liu. Harmonic moments and large deviations for a supercritical branching process in a random environment. Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1199-1202. doi : 10.1016/j.crma.2011.10.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.10.001/

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