1LMBA - Laboratoire de Mathématiques de Bretagne Atlantique (Université de Brest, 6 avenue Le Gorgeu, CS 93837, 29238 Brest cedex 3 / Université de Bretagne-Sud, Centre Yves Coppens, Bât. B, Campus de Tohannic, BP 573, 56017 Vannes - France)
UBO - Université de Brest (Université de Bretagne Occidentale - 3 Rue des Archives 29238, Brest - France)
Abstract : Conditioned on the generating functions of offspring distribution, we study the asymp-totic behaviour of the probability of non-extinction of a critical multi-type Galton-Watson process in i.i.d. random environments by using limits theorems for products of positive random matrices. Under some certain assumptions, the survival probability is proportional to 1/ √ n.
https://hal.archives-ouvertes.fr/hal-01705787 Contributor : Quansheng LiuConnect in order to contact the contributor Submitted on : Friday, February 9, 2018 - 6:01:06 PM Last modification on : Tuesday, January 11, 2022 - 5:56:10 PM
Emile Le Page, Marc Peigné. The survival probability of a critical multi-type branching process in i.i.d. random environment. Annals of Probability, Institute of Mathematical Statistics, 2018, 46 (5), pp.2946-2972. ⟨hal-01705787⟩