Differential equations driven by Gaussian signals

Abstract

We consider multi-dimensional Gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of Lévy area(s). Gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful - yet conceptually simple - framework in which to analyze differential equations driven by Gaussian signals in the rough paths sense. © Association des Publications de l'Institut Henri Poincaré, 2010.