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January 2012 Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior
Achim Klenke, Leonid Mytnik
Ann. Probab. 40(1): 103-129 (January 2012). DOI: 10.1214/10-AOP621

Abstract

Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479–497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.

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Achim Klenke. Leonid Mytnik. "Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior." Ann. Probab. 40 (1) 103 - 129, January 2012. https://doi.org/10.1214/10-AOP621

Information

Published: January 2012
First available in Project Euclid: 3 January 2012

zbMATH: 1244.60088
MathSciNet: MR2917768
Digital Object Identifier: 10.1214/10-AOP621

Subjects:
Primary: 60G17 , 60J55 , 60J65 , 60K35

Keywords: Coexistence , Lévy noise , Mutually catalytic branching , segregation of types , Stochastic differential equations , Trotter product

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 1 • January 2012
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