Branching random walks, stable point processes and regular variation

Ayan Bhattacharya, Rajat Subhra Hazra and Parthanil Roy

Stochastic Processes and their Applications, 2018, vol. 128, issue 1, 182-210

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.

Keywords: Branching random walk; Branching process; Strictly stable; Point process; Cox process; Extreme values; Rightmost point (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:1:p:182-210

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DOI: 10.1016/j.spa.2017.04.009

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