Differential Equations Driven by Gaussian Signals I
Probability
2007-07-04 v1
Abstract
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 constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful - yet conceptually simple - framework in which to analysize differential equations driven by Gaussian signals in the rough paths sense.
Cite
@article{arxiv.0707.0313,
title = {Differential Equations Driven by Gaussian Signals I},
author = {Peter Friz and Nicolas Victoir},
journal= {arXiv preprint arXiv:0707.0313},
year = {2007}
}