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Infinite-dimensional paracontrolled distributions: the Burgers generator

Presented by: 
Nicolas Perkowski Humboldt-Universität zu Berlin
Thursday 6th September 2018 - 10:00 to 11:00
INI Seminar Room 1
Regularity structures, paracontrolled distributions and all that provide pathwise, deterministic tools to solve and study singular stochastic PDEs over finite-dimensional spaces. From a probabilistic point of view we would also like to understand the associated Kolmogorov backward equations, which can be interpreted as infinite-dimensional singular SPDEs. I will discuss on the example of the conservative stochastic Burgers equation how to construct a space of (para-) paracontrolled distributions in which the backward equation is well posed. As an application we obtain a martingale formulation and an alternative proof for the well-posedness of "energy solutions", without using the Cole-Hopf transform. The approach extends to some other singular SPDEs with Gaussian invariant measures and quadratic nonlinearities. This is joint work with Massimiliano Gubinelli.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons