Displaying similar documents to “The Feynman path integral as an improper integral over the Sobolev space”

Differential equations driven by gaussian signals

Peter Friz, Nicolas Victoir (2010)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

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.

Enhanced Gaussian processes and applications

Laure Coutin, Nicolas Victoir (2009)

ESAIM: Probability and Statistics

Similarity:

We propose some construction of enhanced Gaussian processes using Karhunen-Loeve expansion. We obtain a characterization and some criterion of existence and uniqueness. Using rough-path theory, we derive some Wong-Zakai Theorem.