A cyclically catalytic super-Brownian motion

DOI10.1214/aop/1008956694zbMath1017.60099OpenAlexW2083519015MaRDI QIDQ1872207

Klaus Fleischmann, Jie Xiong

Publication date: 6 May 2003

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

Full work available at URL: https://doi.org/10.1214/aop/1008956694

zbMATH Keywords

extinctionmartingale problemcatalystcyclic reactionfinite time survivalglobal segregation of neighboring types

Mathematics Subject Classification ID

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

Related Items (6)

Mutually catalytic branching in the plane: Finite measure states ⋮ A stochastic log-Laplace equation. ⋮ Strong uniqueness for cyclically symbiotic branching diffusions ⋮ Compact interface property for symbiotic branching ⋮ Long-term behaviour of a cyclic catalytic branching system ⋮ Strong uniqueness for a class of singular SDEs for catalytic branching diffusions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An \(\infty\)-dimensional inhomogeneous Langevin's equation
• Flux and fixation in cyclic particle systems
• Application of the superposition principle to the study of CEC, CE, EC and catalytic mechanisms in cyclic chronopotentiometry. III
• Uniqueness for a mutually catalytic branching model
• Cellular automaton growth on \(\mathbb{Z}^2\): Theorems, examples, and problems
• A reaction-diffusion equation for a cyclic system with three components
• Long-time behavior and coexistence in a mutually catalytic branching model
• Spatial aspects of interspecific competition
• Extinction for two parabolic stochastic PDE's on the lattice
• Clustering of linearly interacting diffusions and universality of their long-time limit distribution
• Mutually catalytic branching in the plane: Infinite measure states
• Mutually catalytic branching in the plane: Uniqueness
• Large time behavior of interface solutions to the heat equation with Fisher-Wright white noise
• Spatial gradients enhance persistence of hypercycles
• Recurrence and ergodicity of interacting particle systems
• Cyclic competition of three species in the time periodic and diffusive case
• Probability with Martingales
• ON THE SELECTION OF A MARKOV PROCESS FROM A SYSTEM OF PROCESSES AND THE CONSTRUCTION OF QUASI-DIFFUSION PROCESSES
• Two Contrasting Properties of Solutions for One-Dimensional Stochastic Partial Differential Equations
• An Introduction to Branching Measure-Valued Processes

This page was built for publication: A cyclically catalytic super-Brownian motion