Reflected stochastic differential equations driven by $G$-Brownian motion in non-convex domains

Yiqing Lin; Abdoulaye Soumana Hima

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arXiv · 1703.03238

Reflected stochastic differential equations driven by $G$-Brownian motion in non-convex domains

Yiqing Lin·Abdoulaye Soumana Hima

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

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BibTeX RIS

Yiqing Lin, Abdoulaye Soumana Hima. 2017-03-09. Reflected stochastic differential equations driven by $G$-Brownian motion in non-convex domains. https://arxiv.org/abs/1703.03238

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