Longtime Behavior for Mutually Catalytic Branching with Negative Correlations

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 article 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.
Type de document :
Pré-publication, Document de travail
2011
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https://hal.archives-ouvertes.fr/hal-00706805
Contributeur : Leif Doering <>
Soumis le : lundi 11 juin 2012 - 15:47:12
Dernière modification le : lundi 29 mai 2017 - 14:26:42

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  • HAL Id : hal-00706805, version 1
  • ARXIV : 1109.6105

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UPMC | INSMI | PMA | USPC

Citation

Leif Doering, Leonid Mytnik. Longtime Behavior for Mutually Catalytic Branching with Negative Correlations. 2011. 〈hal-00706805〉

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