48 citations · 119 across the 18 of their papers we have counts for
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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…
Isoperimetry and Rough Path Regularity
Peter Friz, Harald Oberhauser
Optimal sample path properties of stochastic processes often involve generalized Hölder- or variation norms. Following a classical result of Taylor, the exact variation of Brownian…
Densities for Rough Differential Equations under Hoermander's Condition
Thomas Cass, Peter Friz
We consider stochastic differential equations dY=V(Y)dX driven by a multidimensional Gaussian process X in the rough path sense. Using Malliavin Calculus we show that Y(t) admits a…
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…