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Degenerate stochastic differential equations arising from catalytic branching networks
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Richard F. Bass, Department of Mathematics, University of Connecticut
Edwin A. Perkins, Department of Mathematics, The University of British Columbia
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Abstract
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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Full text: PDF
Pages: 1808-1885
Published on: October 4, 2008
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Electronic Journal of Probability. ISSN: 1083-6489 |
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