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May 2010 A Dirichlet process characterization of a class of reflected diffusions
Weining Kang, Kavita Ramanan
Ann. Probab. 38(3): 1062-1105 (May 2010). DOI: 10.1214/09-AOP487


For a class of stochastic differential equations with reflection for which a certain ${\mathbb{L}}^{p}$ continuity condition holds with p>1, it is shown that any weak solution that is a strong Markov process can be decomposed into the sum of a local martingale and a continuous, adapted process of zero p-variation. When p=2, this implies that the reflected diffusion is a Dirichlet process. Two examples are provided to motivate such a characterization. The first example is a class of multidimensional reflected diffusions in polyhedral conical domains that arise as approximations of certain stochastic networks, and the second example is a family of two-dimensional reflected diffusions in curved domains. In both cases, the reflected diffusions are shown to be Dirichlet processes, but not semimartingales.


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Weining Kang. Kavita Ramanan. "A Dirichlet process characterization of a class of reflected diffusions." Ann. Probab. 38 (3) 1062 - 1105, May 2010.


Published: May 2010
First available in Project Euclid: 2 June 2010

zbMATH: 1202.60059
MathSciNet: MR2674994
Digital Object Identifier: 10.1214/09-AOP487

Primary: 60G17 , 60J55
Secondary: 60J65

Keywords: diffusion approximations , Dirichlet processes , Extended Skorokhod problem , generalized processor sharing , reflected Brownian motion , Reflected diffusions , Rough paths , Semimartingales , Skorokhod map , Skorokhod problem , zero energy

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 3 • May 2010
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