Robert Hesse - Solving Stochastic Evolution Equations (almost) without stochastics

We consider a class of infinite-dimensional parabolic evolution equations driven by multiplicative rough stochastic noise. As main example we introduce a Brownian motion. In order to solve these equations in a mild pathwise sense we give a short introduction on rough paths theory. In particular we show how to lift a Brownian motion to a rough path and how to exploit the semigroup's regularity to define a rough integral.

This talk is based on a joint work with Alexandra Neamţu.