Branching random walks, stable point processes and regular variation

Article Type

Research Article

Publication Title

Stochastic Processes and their Applications

Abstract

Using the theory of regular variation, we give a sufficient condition for a point process to be in the superposition domain of attraction of a strictly stable point process. This sufficient condition is used to obtain the weak limit of a sequence of point processes induced by a branching random walk with jointly regularly varying displacements. Because of heavy tails of the step size distribution, we can invoke a one large jump principle at the level of point processes to give an explicit representation of the limiting point process. As a consequence, we extend the main result of Durrett (1983) and verify that two related predictions of Brunet and Derrida (2011) remain valid for this model.

First Page

182

Last Page

210

DOI

10.1016/j.spa.2017.04.009

Publication Date

1-1-2018

Comments

All Open Access, Bronze, Green

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