Jan Maas (University of Bonn)
Title: A spatial version of the It\^o-Stratonovich correction
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.