The Annals of Probability
- Ann. Probab.
- Volume 38, Number 3 (2010), 1062-1105.
A Dirichlet process characterization of a class of reflected diffusions
For a class of stochastic differential equations with reflection for which a certain 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.
Ann. Probab., Volume 38, Number 3 (2010), 1062-1105.
First available in Project Euclid: 2 June 2010
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Reflected Brownian motion reflected diffusions rough paths Dirichlet processes zero energy semimartingales Skorokhod problem Skorokhod map extended Skorokhod problem generalized processor sharing diffusion approximations
Kang, Weining; Ramanan, Kavita. A Dirichlet process characterization of a class of reflected diffusions. Ann. Probab. 38 (2010), no. 3, 1062--1105. doi:10.1214/09-AOP487. https://projecteuclid.org/euclid.aop/1275486188