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An Application of the Backbone Decomposition to Supercritical Super-Brownian Motion with a Barrier

Part of: Representations of solutions Markov processes

Published online by Cambridge University Press:  04 February 2016

A. E. Kyprianou ,
A. Murillo-Salas  and
J. L. Pérez
A. E. Kyprianou*
Affiliation:
University of Bath
A. Murillo-Salas*
Affiliation:
Universidad de Guanajuato
J. L. Pérez*
Affiliation:
Mexico Autonomous Institute of Technology
*
∗ Postal address: Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK.
∗∗ Postal address: Departamento de Matemáticas, Universidad de Guanajuato, Jalisco s/n, Mineral de Valenciana, Guanajuato, Gto. CP 36240, México.
∗∗∗ Postal address: Department of Statistics, Mexico Autonomous Institute of Technology, Rio Hondo 1, Tizapan 1 San Angel, Mexico DF 01000, Mexico.
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Abstract

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We analyse the behaviour of supercritical super-Brownian motion with a barrier through the pathwise backbone embedding of Berestycki, Kyprianou and Murillo-Salas (2011). In particular, by considering existing results for branching Brownian motion due to Harris and Kyprianou (2006) and Maillard (2011), we obtain, with relative ease, conclusions regarding the growth in the right-most point in the support, analytical properties of the associated one-sided Fisher-Kolmogorov-Petrovskii-Piscounov wave equation, as well as the distribution of mass on the exit measure associated with the barrier.

Keywords

Super-Brownian motionbackbone decompositionkilled super-Brownian motion

MSC classification

Primary: 60J68: Superprocesses 35C07: Traveling wave solutions
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 3 , September 2012 , pp. 671 - 684
Copyright
© Applied Probability Trust 

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