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March 2010 A Trotter-type approach to infinite rate mutually catalytic branching
Achim Klenke, Mario Oeler
Ann. Probab. 38(2): 479-497 (March 2010). DOI: 10.1214/09-AOP488


Dawson and Perkins [Ann. Probab. 26 (1988) 1088–1138] constructed a stochastic model of an interacting two-type population indexed by a countable site space which locally undergoes a mutually catalytic branching mechanism. In Klenke and Mytnik [Preprint (2008), arXiv:0901.0623], it is shown that as the branching rate approaches infinity, the process converges to a process that is called the infinite rate mutually catalytic branching process (IMUB). It is most conveniently characterized as the solution of a certain martingale problem. While in the latter reference, a noise equation approach is used in order to construct a solution to this martingale problem, the aim of this paper is to provide a Trotter-type construction.

The construction presented here will be used in a forthcoming paper, Klenke and Mytnik [Preprint (2009)], to investigate the long-time behavior of IMUB (coexistence versus segregation of types).

This paper is partly based on the Ph.D. thesis of the second author (2008), where the Trotter approach was first introduced.


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Achim Klenke. Mario Oeler. "A Trotter-type approach to infinite rate mutually catalytic branching." Ann. Probab. 38 (2) 479 - 497, March 2010.


Published: March 2010
First available in Project Euclid: 9 March 2010

zbMATH: 1191.60112
MathSciNet: MR2642883
Digital Object Identifier: 10.1214/09-AOP488

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

Keywords: Martingale problem , Mutually catalytic branching , Population dynamics , Stochastic differential equations , Trotter formula

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 2 • March 2010
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