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2020 Occupation densities of ensembles of branching random walks
Steven P. Lalley, Si Tang
Electron. Commun. Probab. 25: 1-13 (2020). DOI: 10.1214/20-ECP293

Abstract

We study the limiting occupation density process for a large number of critical and driftless branching random walks. We show that the rescaled occupation densities of $\lfloor sN\rfloor $ branching random walks, viewed as a function-valued, increasing process $\{g_{s}^{N}\}_{s\ge 0}$, converges weakly to a pure jump process in the Skorohod space $\mathbb{D} ([0, +\infty ), \mathcal{C} _{0}(\mathbb{R} ))$, as $N\to \infty $. Moreover, the jumps of the limiting process consist of i.i.d. copies of an Integrated super-Brownian Excursion (ISE) density, rescaled and weighted by the jump sizes in a real-valued stable-1/2 subordinator.

Citation

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Steven P. Lalley. Si Tang. "Occupation densities of ensembles of branching random walks." Electron. Commun. Probab. 25 1 - 13, 2020. https://doi.org/10.1214/20-ECP293

Information

Received: 25 August 2019; Accepted: 22 January 2020; Published: 2020
First available in Project Euclid: 31 January 2020

zbMATH: 1434.60243
MathSciNet: MR4066305
Digital Object Identifier: 10.1214/20-ECP293

Subjects:
Primary: 60G50, 60J80

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