Penalty Method for Obliquely Reflected Diffusions
Probability
2021-08-09 v9
Abstract
Take a multidimensional normally or obliquely reflected diffusion in a smooth domain. Approximate it by solutions of stochastic differential equations without reflection using the penalty method. That is, we approximate the reflection term with an additional drift term. In the existing literature, usually a specific approximating sequence is provided in order to prove existence of a reflected diffusion. In this article, we provide general sufficient conditions on the approximating coefficients.
Cite
@article{arxiv.1509.01777,
title = {Penalty Method for Obliquely Reflected Diffusions},
author = {Andrey Sarantsev},
journal= {arXiv preprint arXiv:1509.01777},
year = {2021}
}
Comments
30 pages. Keywords: reflected diffusion, reflected Brownian motion, stochastic differential equation, oblique reflection, weak convergence, penalty method