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2015 On the scaling limits of Galton-Watson processes in varying environments
Vincent Bansaye, Florian Simatos
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Electron. J. Probab. 20: 1-36 (2015). DOI: 10.1214/EJP.v20-3812


;We establish a general sufficient condition for a sequence of Galton-Watson branching processes in varying environments to converge weakly. This condition extends previous 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.


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Vincent Bansaye. Florian Simatos. "On the scaling limits of Galton-Watson processes in varying environments." Electron. J. Probab. 20 1 - 36, 2015.


Accepted: 3 July 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1321.60171
MathSciNet: MR3371434
Digital Object Identifier: 10.1214/EJP.v20-3812

Primary: 60F17
Secondary: 60J80, 60K37


Vol.20 • 2015
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