Differential Equations Driven by Gaussian Signals I

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132862We consider multi-dimensional Gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of stochastic 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 analysize differential equations driven by Gaussian signals in the rough paths sense.Probability60G15; 60H99Differential Equations Driven by Gaussian Signals Itext