Invariance for Rough Differential Equations

Laure Coutin; Nicolas Marie

doi:10.1016/j.spa.2016.11.002

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arXiv · 1601.03535

Invariance for Rough Differential Equations

Laure Coutin·Nicolas Marie

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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 $\mathbb R^d$ ($d\in\mathbb N^*$) 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.

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Laure Coutin, Nicolas Marie. 2016-11-23. Invariance for Rough Differential Equations. https://doi.org/10.1016/j.spa.2016.11.002

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