Long-time behavior and coexistence in a mutually catalytic branching model

DOI10.1214/aop/1022855746zbMath0938.60042OpenAlexW2003284619MaRDI QIDQ1307478

Edwin A. Perkins, Donald A. Dawson

Publication date: 31 October 1999

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1022855746

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Diffusion processes (60J60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Random measures (60G57) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (21)

A cyclically catalytic super-Brownian motion ⋮ Mutually catalytic branching in the plane: Finite measure states ⋮ The scaling limit of the interface of the continuous-space symbiotic branching model ⋮ Phase transitions for the long-time behavior of interacting diffusions ⋮ Longtime Behavior for Mutually Catalytic Branching with Negative Correlations ⋮ Infinite rate symbiotic branching on the real line: the tired frogs model ⋮ Infinite rate mutually catalytic branching in infinitely many colonies: construction, characterization and convergence ⋮ On the moments and the interface of the symbiotic branching model ⋮ Properties of the parabolic Anderson model and the Anderson polymer model ⋮ Infinite rate mutually catalytic branching in infinitely many colonies: the longtime behavior ⋮ Stationary distributions for dioecious branching particle systems with rapid stirring ⋮ A Trotter-type approach to infinite rate mutually catalytic branching ⋮ Intermittency and ageing for the symbiotic branching model ⋮ Strong uniqueness for cyclically symbiotic branching diffusions ⋮ Compact interface property for symbiotic branching ⋮ Infinite rate mutually catalytic branching ⋮ The renormalization transformation for two-type branching models ⋮ Strong uniqueness for a class of singular SDEs for catalytic branching diffusions ⋮ A new look at duality for the symbiotic branching model ⋮ A conversation with Don Dawson ⋮ Mutually interacting superprocesses with migration

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