Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior

Achim Klenke; Leonid Mytnik

doi:10.1214/10-AOP621

Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior

Achim Klenke, Leonid Mytnik

Data and Decision Sciences

Research output: Contribution to journal › Article › peer-review

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 recur- rent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.

Original language	English
Pages (from-to)	103-129
Number of pages	27
Journal	Annals of Probability
Volume	40
Issue number	1
DOIs	https://doi.org/10.1214/10-AOP621
State	Published - Jan 2012

Keywords

Coexistence
Lévy noise
Mutually catalytic branching
Segregation of types
Stochastic differential equations
Trotter product

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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KW - Coexistence

KW - Lévy noise

KW - Mutually catalytic branching

KW - Segregation of types

KW - Stochastic differential equations

KW - Trotter product

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Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior

Abstract

Keywords

ASJC Scopus subject areas

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