Invariance for rough differential equations

Laure Coutin and Nicolas Marie

Stochastic Processes and their Applications, 2017, vol. 127, issue 7, 2373-2395

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 Rd (d∈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.

Keywords: Viability theorem; Comparison theorem; Rough differential equations; Fractional Brownian motion; Logistic equation (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spa.2016.11.002

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