Differential Equations Driven by Gaussian Signals

15 January 2007
Dr Peter Fritz
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.)  
  • Stochastic Analysis Seminar