Branching random walks, stable point processes and regular variation

Bhattacharya, Ayan ; Hazra, Rajat Subhra ; Roy, Parthanil (2018) Branching random walks, stable point processes and regular variation Stochastic Processes and their Applications, 128 (1). pp. 182-210. ISSN 0304-4149

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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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier B.V..
Keywords:Branching Random Walk; Branching Process; Strictly Stable; Point Process; Cox Process; Extreme Values; Rightmost Point.
ID Code:121030
Deposited On:08 Jul 2021 11:48
Last Modified:08 Jul 2021 11:48

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