168 citations · 436 across the 32 of their papers we have counts for
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A Lévy area by Fourier normal ordering for multidimensional fractional Brownian motion with small Hurst index
Jeremie Unterberger
The main tool for stochastic calculus with respect to a multidimensional process with small Hölder regularity index is rough path theory. Once has been lifted to a rough pa…
Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion
Jérémie Unterberger
As a general rule, differential equations driven by a multi-dimensional irregular path are solved by constructing a rough path over . The domain of definition ? and also est…
Hölder-continuous rough paths by Fourier normal ordering
J. Unterberger
We construct in this article an explicit geometric rough path over arbitrary -dimensional paths with finite -variation for any . The method may be coined as 'Fou…
Discretizing the fractional Levy area
Andreas Neuenkirch, Samy Tindel, Jérémie Unterberger
In this article, we give sharp bounds for the Euler- and trapezoidal discretization of the Levy area associated to a d-dimensional fractional Brownian motion. We show that there ar…
A rough path over multidimensional fractional Brownian motion with arbitrary Hurst index by Fourier normal ordering
Jeremie Unterberger
Fourier normal ordering \cite{Unt09bis} is a new algorithm to construct explicit rough paths over arbitrary Hölder-continuous multidimensional paths. We apply in this article the F…