The Annals of Probability

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

E. Le Page, M. Peigné, and C. Pham

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Abstract

We study the asymptotic behaviour of the probability of non-extinction of a critical multi-type Galton–Watson process in i.i.d. random environments by using limit theorems for products of positive random matrices. Under suitable assumptions, the survival probability is proportional to $1/\sqrt{n}$.

Article information

Source
Ann. Probab., Volume 46, Number 5 (2018), 2946-2972.

Dates
Received: October 2016
Revised: November 2017
First available in Project Euclid: 24 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.aop/1535097643

Digital Object Identifier
doi:10.1214/17-AOP1243

Mathematical Reviews number (MathSciNet)
MR3846842

Zentralblatt MATH identifier
06964352

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F17: Functional limit theorems; invariance principles 60K37: Processes in random environments

Keywords
Multi-type branching process survival probability random environment product of random matrices critical case

Citation

Le Page, E.; Peigné, M.; Pham, C. The survival probability of a critical multi-type branching process in i.i.d. random environment. Ann. Probab. 46 (2018), no. 5, 2946--2972. doi:10.1214/17-AOP1243. https://projecteuclid.org/euclid.aop/1535097643


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