Harmonic moments and large deviations for a supercritical branching process in a random environment

Huang, Chunmao; Liu, Quansheng

doi:10.1016/j.crma.2011.10.001

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]

Présenté par : the Editorial Board

Huang, Chunmao ^1,² ; Liu, Quansheng ^1,²

¹ Université de Bretagne-Sud, LMAM, campus de Tohannic, BP 573, 56017 Vannes, France
² Université Européenne de Bretagne, France

Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1199-1202.

Résumé
Abstract

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

Let $(Z_{n})$ be a supercritical branching process in a random environment ξ, and W be the limit of the normalized population size $Z_{n} / E [Z_{n} | ξ]$ . We show large and moderate deviation principles for the sequence $\log Z_{n}$ (with appropriate normalization) by finding an equivalence of the moments of $Z_{n}$ and a criterion for the existence of harmonic moments of W.

Reçu le : 2011-07-29
Accepté le : 2011-10-03
Publié le : 2011-10-22

DOI : 10.1016/j.crma.2011.10.001

Affiliations des auteurs :

Huang, Chunmao ^{1, 2} ; Liu, Quansheng ^{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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     title = {Harmonic moments and large deviations for a supercritical branching process in a random environment},
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     pages = {1199--1202},
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Huang, Chunmao; Liu, Quansheng. Harmonic moments and large deviations for a supercritical branching process in a random environment. Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1199-1202. doi : 10.1016/j.crma.2011.10.001. http://www.numdam.org/articles/10.1016/j.crma.2011.10.001/

Bibliographie
Cité par

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