Reflected rough differential equations

Shigeki Aida

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arXiv · 1311.6104

Reflected rough differential equations

Shigeki Aida

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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.

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Shigeki Aida. 2015-04-23. Reflected rough differential equations. https://arxiv.org/abs/1311.6104

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