Rough evolution equations

Abstract

We generalize Lyons' rough paths theory in order to give a pathwise meaning to some nonlinear infinite-dimensional evolution equation associated to an analytic semigroup and driven by an irregular noise. As an illustration, we discuss a class of linear and nonlinear 1d SPDEs driven by a space-time Gaussian noise with singular space covariance and Brownian time dependence. © Institute of Mathematical Statistics, 2010.