Infinite rate mutually catalytic branching

Abstract

Consider the mutually catalytic branching process with finite branching rate $\gamma$. We show that as $\gamma \to \infty$, 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.

Published in at http://dx.doi.org/10.1214/09-AOP520 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• A Trotter-type approach to infinite rate mutually catalytic branching
• Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior

Cited by in corpus (5)

• A Trotter-type approach to infinite rate mutually catalytic branching
• Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior
• The scaling limit of the interface of the continuous-space symbiotic branching model
• The symbiotic branching model: duality and interfaces
• Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence