2016/01/31 by Laure Coutin, Nicolas Marie · 7 citations
Economics, Econometrics and Finance · Mathematics · #Brownian motion #Differential (mechanical device) #Differential equation #Extension (predicate logic) #Fractional Brownian motion #Geometry #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Physics #Regular polygon #Statistics #Stochastic differential equation #Stochastic partial differential equation #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60H10
paper · pdf · doi:10.1016/j.spa.2016.11.002
published in Stochastic Processes and their Applications 127(7), 2373-2395 (Elsevier BV) · 22 pages
arxiv created 2016/11/23 · openalex publication_date 2016/12/02 · arxiv updated 2019/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Rd (d∈\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.