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SUMMARY:Infinite-dimensional paracontrolled distributions: the Burgers gen
 erator - Nicolas Perkowski (Humboldt-Universität zu Berlin)
DTSTART:20180906T090000Z
DTEND:20180906T100000Z
UID:TALK109267@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Regularity structures\, paracontrolled distributions and all t
 hat provide pathwise\, deterministic tools to solve and study singular sto
 chastic 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 SPDE
 s. I will discuss on the example of the conservative stochastic Burgers eq
 uation 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 e
 xtends to some other singular SPDEs with Gaussian invariant measures and q
 uadratic nonlinearities. This is joint work with Massimiliano Gubinelli.
LOCATION:Seminar Room 1\, Newton Institute
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