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

2017/03/09 by Yiqing Lin, Lin, Yiqing, Abdoulaye Soumana Hima +1 · 1 citation
Economics, Econometrics and Finance · Computer Science · #Stochastic processes and financial applications #Advanced Mathematical Modeling in Engineering

paper · doi:10.48550/arxiv.1703.03238

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-Hölder 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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• Backward Stochastic Volterra integral equations driven by G-Brownian motion

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