We consider Burgers type stochastic PDEs in one space dimension driven by multiplicative space-time white noise. These equations turn out to be very unstable under approximation of the nonlinearity. In fact, we prove that solutions to different - seemingly natural - approximating schemes converge to different limits. This phenomenon can be explained naturally in the framework of rough paths theory.
This is joint work with Martin Hairer and Hendrik Weber (Warwick).
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