Reflected rough differential equations

Abstract

In this paper, we study reflected differential equations driven by continuous paths with finite $p$-variation ($1\le p<2$) and $p$-rough paths ($2\le p<3$) on domains in Euclidean spaces whose boundaries may not be smooth. We define reflected rough differential equations and prove the existence of a solution. Also we discuss the relation between the solution to reflected stochastic differential equation and reflected rough differential equation when the driving process is a Brownian motion.

arXiv commentThis will appear in Stochastic Processes and their applications. doi:10.1016/j.spa.2015.03.008

Cited by in corpus (1)

• Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces II