The longtime behavior of branching random walk in a catalytic medium
Greven A, Klenke A, Wakolbinger A (1999)
Publication Type: Journal article, Original article
Publication year: 1999
Journal
Publisher: Institute of Mathematical Statistics (IMS): OAJ / Institute of Mathematical Statistics
Book Volume: 4
Pages Range: 80 pp.
Journal Issue: 12
URI: https://projecteuclid.org/euclid.ejp/1457125521
DOI: 10.1214/EJP.v4-49
Abstract
We consider catalytic branching random walk (the reactant) where the state space is a countable Abelean group. The branching is critical binary and the local branching rate is given by a catalytic medium. Here the medium is itself an autonomous (ordinary) branching random walk (the catalyst) - maybe with a different motion law. For persistent catalyst (transient motion) the reactant shows the usual dichotomy of persistence versus extinction depending on transience or recurrence of its motion. If the catalyst goes to local extinction it turns out that the longtime behaviour of the reactant ranges (depending on its motion) from local extinction to free random walk with either deterministic or random global intensity of particles.
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Germany (DE)How to cite
APA:
Greven, A., Klenke, A., & Wakolbinger, A. (1999). The longtime behavior of branching random walk in a catalytic medium. Electronic Journal of Probability, 4(12), 80 pp.. https://dx.doi.org/10.1214/EJP.v4-49
MLA:
Greven, Andreas, Achim Klenke, and Anton Wakolbinger. "The longtime behavior of branching random walk in a catalytic medium." Electronic Journal of Probability 4.12 (1999): 80 pp.
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