English

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 α\alpha-H\"older continuous functions. With the help of these results obtained previously for deterministic problems, we pathwisely define the reflected GG-Brownian motion and prove its existence and uniqueness in a Banach space. Finally, multi-dimensional reflected stochastic differential equations driven by GG-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}
}