Differential Equations Driven by Gaussian Signals I

Details Differential Equations Driven by Gaussian Signals I Differential Equations Driven by Gaussian Signals I

2007-07-02

arxiv.org/abs/0707.0313v1

Mathematics

Probability

Scientific paper

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.

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