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Catalytic branching and the Brownian snake

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  • Klenke, Achim

Abstract

We construct a catalytic super process X (measure-valued spatial branching process) where the local branching rate is governed by an additive functional A of the motion process. These processes have been investigated before but under restrictive assumptions on A. Here we do not even need continuity of A. The key is to introduce a new time scale in which motion and branching occur at a varying speed but are continuous. Another aspect is to consider X in the generic time scale of the branching--and not of the motion process. This allows to give an explicit construction of X using the Brownian snake. As a by-product this yields an almost sure approximation by the corresponding branching particle systems.

Suggested Citation

  • Klenke, Achim, 2003. "Catalytic branching and the Brownian snake," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 211-235, February.
    • Handle: RePEc:eee:spapps:v:103:y:2003:i:2:p:211-235
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    Cited by:

    1. Mörters, Peter & Vogt, Pascal, 2005. "A construction of catalytic super-Brownian motion via collision local time," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 77-90, January.
    2. Delmas, Jean-François & Dhersin, Jean-Stéphane, 2003. "Super Brownian motion with interactions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 301-325, October.

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