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On the scaling limits of Galton–Watson processes in varying environments

Bansaye, Vincent and Simatos, Florian On the scaling limits of Galton–Watson processes in varying environments. (2015) Electronic Journal of Probability, 20 (75). 1-36.

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Official URL: https://doi.org/10.1214/EJP.v20-3812

Abstract

We establish a general sufficient condition for a sequence of Galton–Watson branching processes in varying environments to converge weakly. This condition extends previ- ous results by allowing offspring distributions to have infinite variance. Our assumptions are stated in terms of pointwise convergence of a triplet of two real- valued functions and a measure. The limiting process is characterized by a backwards integro-differential equation satisfied by its Laplace exponent, which generalizes the branching equation satisfied by continuous state branching processes. Several examples are discussed, namely branching processes in random environment, Feller diffusion in varying environments and branching processes with catastrophes.

Item Type:Article
HAL Id:hal-01890532
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Ecole Polytechnique (FRANCE)
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Deposited By: Florian Simatos
Deposited On:08 Oct 2018 14:51

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