Jan Maas (University of Bonn)

Title:  A spatial version of the It\^o-Stratonovich correction


We consider stochastic Burgers type equations in one space dimension perturbed by space-time white noise. Although these equations are perfectly well-posed, it turns out that different natural approximation schemes converge to different limits. The limiting equations contain correction terms that arise due to the spatial roughness of the solutions, in a similar spirit as the usual It\^o-Stratonovich corrections arising in temporal discretisations of stochastic ODEs. We shall discuss how the theory of rough paths provides a natural framework for these results.
This is based on joint work with Martin Hairer and Hendrik Weber.