Seminar series
Date
Mon, 15 Jan 2007
14:15
14:15
Location
DH 3rd floor SR
Speaker
Dr Peter Fritz
Organisation
University of Cambridge
We consider multi-dimensional Gaussian processes and give a novel, simple and
sharp condition on its covariance (finiteness of its two dimensional rho-variation,
for some rho <2) for the existence of "natural" Levy areas and higher iterated
integrals, and subsequently the existence of Gaussian rough paths. We prove a
variety of (weak and strong) approximation results, large deviations, and
support description.
Rough path theory then gives a theory of differential equations driven by
Gaussian signals with a variety of novel continuity properties, large deviation
estimates and support descriptions generalizing classical results of
Freidlin-Wentzell and Stroock-Varadhan respectively.
(Joint work with Nicolas Victoir.)