Invariance for Rough Differential Equations

Abstract

In 1990, in Itô's stochastic calculus framework, Aubin and Da Prato established a necessary and sufficient condition of invariance of a nonempty compact or convex subset $C$ of ${\mathbb{R}}^d$ ($d\in {\mathbb{N}}^{\ast }$) for stochastic differential equations (SDE) driven by a Brownian motion. In Lyons rough paths framework, this paper deals with an extension of Aubin and Da Prato's 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.

22 pages

References in corpus (3)

• Stochastic viability and comparison theorems for mixed stochastic differential equations
• Validating Stochastic Models: Invariance Criteria for Systems of Stochastic Differential Equations and the Selection of a Stochastic Hodgkin-Huxley Type Model
• Another proof for the equivalence between invariance of closed sets with respect to stochastic and deterministic systems

Cited by in corpus (1)

• Invariant submanifolds for solutions to rough differential equations