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.
"Rough evolution equations." Ann. Probab. 38 (1) 1 - 75, January 2010. https://doi.org/10.1214/08-AOP437