Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7550469 | Stochastic Processes and their Applications | 2018 | 29 Pages |
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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Ayan Bhattacharya, Rajat Subhra Hazra, Parthanil Roy,