Let be a supercritical branching process in a random environment ξ, and W be the limit of the normalized population size . We show large and moderate deviation principles for the sequence (with appropriate normalization) by finding an equivalence of the moments of and a criterion for the existence of harmonic moments of W.
Soient un processus de branchement sur-critique dans un environnement aléatoire ξ, et W la limite de la population normalisée . Nous montrons les principes de grande déviation et de déviation modérée pour la suite en trouvant un équivalent des moments de et un critère pour lʼexistence des moments harmoniques de W.
Accepted:
Published online:
Chunmao Huang 1, 2; Quansheng Liu 1, 2
@article{CRMATH_2011__349_21-22_1199_0, author = {Chunmao Huang and Quansheng Liu}, title = {Harmonic moments and large deviations for a supercritical branching process in a random environment}, journal = {Comptes Rendus. Math\'ematique}, pages = {1199--1202}, publisher = {Elsevier}, volume = {349}, number = {21-22}, year = {2011}, doi = {10.1016/j.crma.2011.10.001}, language = {en}, }
TY - JOUR AU - Chunmao Huang AU - Quansheng Liu TI - Harmonic moments and large deviations for a supercritical branching process in a random environment JO - Comptes Rendus. Mathématique PY - 2011 SP - 1199 EP - 1202 VL - 349 IS - 21-22 PB - Elsevier DO - 10.1016/j.crma.2011.10.001 LA - en ID - CRMATH_2011__349_21-22_1199_0 ER -
%0 Journal Article %A Chunmao Huang %A Quansheng Liu %T Harmonic moments and large deviations for a supercritical branching process in a random environment %J Comptes Rendus. Mathématique %D 2011 %P 1199-1202 %V 349 %N 21-22 %I Elsevier %R 10.1016/j.crma.2011.10.001 %G en %F CRMATH_2011__349_21-22_1199_0
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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