Brownian motion

Donsker theorem for rough paths

Rough paths were introduced by Lyons in 1998 to cope with the non-continuity of the Itô map (the map which sends a sample-path of the Brownian motion to the solution of an SDE driven by this path). The so-called enriched Brownian motion is the couple made by the Brownian itself and its Lévy area. It is thus a natural question to enrich the Donsker theorem and see if the adjunction of this new component does change the convergence rate we established earlier.

Stein's method for Brownian approximations