Longtime Behavior for Mutually Catalytic Branching with Negative Correlations

Leif Döring, Leonid Mytnik

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In several examples, dualities for interacting diffusion and particle systems permit the study of the longtime behavior of solutions. A particularly difficult model in which many techniques collapse is a two-type model with mutually catalytic interaction introduced by Dawson/Perkins for which they proved under some assumptions a dichotomy between extinction and coexistence directly from the defining equations.In the present chapter we show how to prove a precise dichotomy for a related model with negatively correlated noises. The proof uses moment bounds on exit times of correlated Brownian motions from the first quadrant and explicit second moment calculations. Since the uniform integrability bound is independent of the branching rate our proof can be extended to infinite branching rate processes.

Original languageEnglish
Title of host publicationAdvances in Superprocesses and Nonlinear PDEs
Pages93-111
Number of pages19
DOIs
StatePublished - 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume38
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Keywords

  • Branching process
  • Duality
  • Longtime Behavior
  • Planar Brownian Motion

ASJC Scopus subject areas

  • General Mathematics

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