Open Access
July 2010 Infinite rate mutually catalytic branching
Achim Klenke, Leonid Mytnik
Ann. Probab. 38(4): 1690-1716 (July 2010). DOI: 10.1214/09-AOP520


Consider the mutually catalytic branching process with finite branching rate γ. We show that as γ → ∞, this process converges in finite-dimensional distributions (in time) to a certain discontinuous process. We give descriptions of this process in terms of its semigroup in terms of the infinitesimal generator and as the solution of a martingale problem. We also give a strong construction in terms of a planar Brownian motion from which we infer a path property of the process.

This is the first paper in a series or three, wherein we also construct an interacting version of this process and study its long-time behavior.


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Achim Klenke. Leonid Mytnik. "Infinite rate mutually catalytic branching." Ann. Probab. 38 (4) 1690 - 1716, July 2010.


Published: July 2010
First available in Project Euclid: 8 July 2010

zbMATH: 1204.60081
MathSciNet: MR2663642
Digital Object Identifier: 10.1214/09-AOP520

Primary: 60J35 , 60J65 , 60J80 , 60K35 , 60K37

Keywords: Martingale problem , Mutually catalytic branching , Stochastic differential equations , strong construction

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 4 • July 2010
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