178 citations · 245 across the 15 of their papers we have counts for
15 papers
A note on higher dimensional -variation
Peter Friz, Nicolas Victoir
We discuss -variation regularity of real-valued functions defined on , based on rectangular increments. When , there are two slightly different notions of -vari…
Differential Equations Driven by Gaussian Signals II
Peter Friz, Nicolas Victoir
Large classes of multi-dimensional Gaussian processes can be enhanced with stochastic Levy area(s). In a previous paper, we gave sufficient and essentially necessary conditions, on…
Good rough path sequences and applications to anticipating stochastic calculus
Laure Coutin, Peter Friz, Nicolas Victoir
We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fi…
Differential Equations Driven by Gaussian Signals I
Peter Friz, Nicolas Victoir
We 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 con…
Non-degeneracy of Wiener functionals arising from rough differential equations
Thomas Cass, Peter Friz, Nicolas Victoir
Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Ito map obtained by solving stochastic differential equations. Rough…
On Uniformly Subelliptic Operators and Stochastic Area
Peter Friz, Nicolas Victoir
We consider uniformly subelliptic operators on certain unimodular Lie groups of polynomial growth. It was shown by Saloff-Coste and Stroock that classical results of De Giorgi, Nas…