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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

Abstract

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.

Citation

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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. https://doi.org/10.1214/09-AOP488

Information

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

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

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

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 2 • March 2010
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