We consider Burgers-type equations driven by space-time white noise that arise naturally as the Langevin equations associated to a diffusion measure. Classically, the solutions to such equations are too irregular for the nonlinearity to be well-defined, even in a weak sense. We show that, using the theory of rough paths, it is nevertheless possible to give a meaning to the notion of solution and we show that such solutions arise as limits of a natural class of smooth approximations.
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