Reflected stochastic differential equations driven by $G$-Brownian motion in non-convex domains
Probability
2017-03-10 v1
Abstract
In this paper, we first review the penalization method for solving deterministic Skorokhod problems in non-convex domains and establish estimates for problems with -H\"older continuous functions. With the help of these results obtained previously for deterministic problems, we pathwisely define the reflected -Brownian motion and prove its existence and uniqueness in a Banach space. Finally, multi-dimensional reflected stochastic differential equations driven by -Brownian motion are investigated via a fixed-point argument.
Keywords
Cite
@article{arxiv.1703.03238,
title = {Reflected stochastic differential equations driven by $G$-Brownian motion in non-convex domains},
author = {Yiqing Lin and Abdoulaye Soumana Hima},
journal= {arXiv preprint arXiv:1703.03238},
year = {2017}
}