TY - JOUR

T1 - Branching random walk in an inhomogeneous breeding potential

AU - Bocharov, Sergey

AU - Harris, Simon C.

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2014.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84926679217&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-11970-0_1

DO - 10.1007/978-3-319-11970-0_1

M3 - Article

AN - SCOPUS:84926679217

SN - 0075-8434

VL - 2123

SP - 1

EP - 32

JO - Lecture Notes in Mathematics

JF - Lecture Notes in Mathematics

ER -