Branching random walk in an inhomogeneous breeding potential

Sergey Bocharov, Simon C. Harris

Research output: Contribution to journalArticle

Abstract

We consider a continuous-time branching random walk in the inhomogeneous breeding potential β│ │p, where β > 0, p ≥ 0. We prove that the population almost surely explodes in finite time if p > 1 and doesn’t explode if p ≤ 1. In the non-explosive cases, we determine the asymptotic behaviour of the rightmost particle.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalSéminaire de Probabilités
VolumeXLVI
DOIs
Publication statusPublished - 30 Oct 2014

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