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Infinite-dimensional paracontrolled distributions: the Burgers generator

Presented by: 
Nicolas Perkowski Humboldt-Universität zu Berlin
Date: 
Thursday 6th September 2018 - 10:00 to 11:00
Venue: 
INI Seminar Room 1
Abstract: 
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.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons