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The survival probability of a critical multi-type branching process in i.i.d. random environment

Emile Le Page 1 Marc Peigné 2
1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
2 LMPT - Laboratoire de Mathématiques et Physique Théorique
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.
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https://hal.archives-ouvertes.fr/hal-01705787
Contributor : Quansheng Liu <>
Submitted on : Friday, February 9, 2018 - 6:01:06 PM
Last modification on : Wednesday, April 1, 2020 - 1:57:30 AM

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  • HAL Id : hal-01705787, version 1

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Emile Le Page, Marc Peigné. The survival probability of a critical multi-type branching process in i.i.d. random environment. Annals of Probability, 2018, 46 (5), pp.2946-2972. ⟨hal-01705787⟩

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