A martingale approach to generalized stochastic Burgers equations
By now there exist very powerful and general solution theories for singular SPDEs, based on regularity structures and related pathwise theories. But the evolution of the laws of these equations is still poorly understood because the usual probabilistic tools break down. In my talk, I will present a martingale theory for a class of singular SPDEs of Burgers type. We construct a domain of controlled (and non-smooth) test functions for the infinitesimal generator and based on that we study the Kolmogorov forward and backward equations and the martingale problem. In combination with works by Goncalves, Jara, Sethuraman and others this leads to weak universality results for generalized stochastic Burgers equations, extending the by now classical weak KPZ universality. Joint work with Massimiliano Gubinelli.