Catalytic branching and the Brownian snake

Achim Klenke

Stochastic Processes and their Applications, 2003, vol. 103, issue 2, 211-235

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.

Keywords: Brownian; snake; Catalytic; branching; Brownian; motion; Catalytic; super; Brownian; motion; Measure-valued; processes; Generic; time; scale; Embedded; particle; system; Catalytic; super; process (search for similar items in EconPapers)
Date: 2003
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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