Partial differential equations driven by rough paths ∗

@inproceedings{Caruana2009PartialDE,
  title={Partial differential equations driven by rough paths ∗},
  author={Michael Caruana and Peter Friz},
  year={2009}
}
We study a class of linear first and second order partial differential equations driven by weak geometric p-rough paths, and prove the existence of a unique solution for these equations. This solution depends continuously on the driving rough path. This allows a robust approach to stochastic partial differential equations. In particular, we may replace Brownian motion by more general Gaussian and Markovian noise. Support theorems and large deviation statements all became easy corollaries of the… CONTINUE READING