Catalytic branching and the Brownian snake
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.
Year of publication: |
2003
|
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Authors: | Klenke, Achim |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 103.2003, 2, p. 211-235
|
Publisher: |
Elsevier |
Keywords: | Brownian snake Catalytic branching Brownian motion Catalytic super Brownian motion Measure-valued processes Generic time scale Embedded particle system Catalytic super process |
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