Abstract
Weak uniqueness is established for the martingale problem associated to a family of catalytic branching networks. This martingale problem corresponds to a stochastic differential equation with a degenerate Hölder continuous diffusion matrix. Our approach uses the semigroup perturbation method of Stroock and Varadhan and a modification of a Banach space of weighted Hölder continuous functions introduced by Bass and Perkins.
Citation
D. A. Dawson. E. A. Perkins. "On the uniqueness problem for catalytic branching networks and other singular diffusions." Illinois J. Math. 50 (1-4) 323 - 383, 2006. https://doi.org/10.1215/ijm/1258059478
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