Viability for Rough Differential Equations

Laure Coutin, Nicolas Marie

Published 2016-01-14Version 1

In 1990, in It\^o stochastic calculus framework, Aubin and DaPrato established a necessary and sufficient condition of invariance of a nonempty compact or convex subset $C$ of $\mathbb R^d$ ($d\in\mathbb N^*$) for stochastic differential equations driven by a Brownian motion. In Lyons rough paths framework, this paper deals with an extension of Aubin and DaPrato results to rough differential equations. A comparison theorem is provided, and the special case of differential equations driven by a fractional Brownian motion is detailed.