Illinois Journal of Mathematics

On the uniqueness problem for catalytic branching networks and other singular diffusions

D. A. Dawson and E. A. Perkins

Full-text: Open access

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.

Article information

Source
Illinois J. Math., Volume 50, Number 1-4 (2006), 323-383.

Dates
First available in Project Euclid: 12 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258059478

Digital Object Identifier
doi:10.1215/ijm/1258059478

Mathematical Reviews number (MathSciNet)
MR2247832

Zentralblatt MATH identifier
1107.60045

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Citation

Dawson, D. A.; Perkins, E. A. On the uniqueness problem for catalytic branching networks and other singular diffusions. Illinois J. Math. 50 (2006), no. 1-4, 323--383. doi:10.1215/ijm/1258059478. https://projecteuclid.org/euclid.ijm/1258059478


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