Differential equations driven by gaussian signals
Peter Friz, Nicolas Victoir (2010)
Annales de l'I.H.P. Probabilités et statistiques
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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.