Bhattacharya, Ayan ; Hazra, Rajat Subhra ; Roy, Parthanil (2017) Point process convergence for branching random walks with regularly varying steps Annales de l'Institut Henri Poincare (B): Probability and Statistics, 53 (2). pp. 802-818. ISSN 0246-0203
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Official URL: http://doi.org/10.1214/15-AIHP737
Related URL: http://dx.doi.org/10.1214/15-AIHP737
Abstract
We consider the limiting behaviour of the point processes associated with a branching random walk with supercritical branching mechanism and balanced regularly varying step size. Assuming that the underlying branching process satisfies Kesten–Stigum condition, it is shown that the point process sequence of properly scaled displacements coming from the n th generation converges weakly to a Cox cluster process. In particular, we establish that a conjecture of (J. Stat. Phys. 143 (3) (2011) 420–446) remains valid in this setup, investigate various other issues mentioned in their paper and recover the main result of (Z. Wahrsch. Verw. Gebiete 62 (2) (1983) 165–170) in our framework.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Branching Random Walk; Cox Process; Extreme Value Theory; Galton–Watson Process; Maxima; Point Process. |
| ID Code: | 121035 |
| Deposited On: | 08 Jul 2021 12:06 |
| Last Modified: | 08 Jul 2021 12:06 |
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