Journal of Applied Probability

An application of the backbone decomposition to supercritical super-Brownian motion with a barrier

A. E. Kyprianou, A. Murillo-Salas, and J. L. Pérez

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Abstract

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.

Article information

Source
J. Appl. Probab. Volume 49, Number 3 (2012), 671-684.

Dates
First available in Project Euclid: 6 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1346955325

Digital Object Identifier
doi:10.1239/jap/1346955325

Mathematical Reviews number (MathSciNet)
MR3012091

Zentralblatt MATH identifier
1278.60127

Subjects
Primary: 60J68: Superprocesses 35C07: Traveling wave solutions

Keywords
Super-Brownian motion backbone decomposition killed super-Brownian motion

Citation

Kyprianou, A. E.; Murillo-Salas, A.; Pérez, J. L. An application of the backbone decomposition to supercritical super-Brownian motion with a barrier. J. Appl. Probab. 49 (2012), no. 3, 671--684. doi:10.1239/jap/1346955325. https://projecteuclid.org/euclid.jap/1346955325


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