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2008 Degenerate stochastic differential equations arising from catalytic branching networks
Richard Bass, Edwin Perkins
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Electron. J. Probab. 13: 1808-1885 (2008). DOI: 10.1214/EJP.v13-568


We establish existence and uniqueness for the martingale problem associated with a system of degenerate SDE's representing a catalytic branching network. The drift and branching coefficients are only assumed to be continuous and satisfy some natural non-degeneracy conditions. We assume at most one catalyst per site as is the case for the hypercyclic equation. Here the two-dimensional case with affine drift is required in work of [DGHSS] on mean fields limits of block averages for 2-type branching models on a hierarchical group. The proofs make use of some new methods, including Cotlar's lemma to establish asymptotic orthogonality of the derivatives of an associated semigroup at different times, and a refined integration by parts technique from [DP1].


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Richard Bass. Edwin Perkins. "Degenerate stochastic differential equations arising from catalytic branching networks." Electron. J. Probab. 13 1808 - 1885, 2008.


Accepted: 4 October 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60070
MathSciNet: MR2448130
Digital Object Identifier: 10.1214/EJP.v13-568

Primary: 60H10
Secondary: 35R15 , 60H30

Keywords: Catalytic branching , Cotlar's lemma , Degenerate diffusions , Martingale problem , perturbations , resolvents , Stochastic differential equations

Vol.13 • 2008
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