Description
A general paracontrolled ansatz for singular SPDE
In this talk, we will present the paracontrolled approach to singular SPDEs and discuss its main ingredients. This framework enables us to give a definition for the ill-posed non-linearities from the equation at hand, and perform a fixed point argument in some suitable space of paracontrolled distributions. We will try to genaralize these ideas in order to construct a general paracontrolled ansatz for a broad class of subcritical SPDEs. A key ingredient in this construction is a family of stochastic fields indexed by decorated trees possessing good analytical and algebraic properties, we then estalish a paralinearisation formula for functions that are paracontrolled with respect to these fields. The singular products appearing in the equation are defined through a genarlised correcor lemma.
This talk is based on a joint work with Yvain Bruned.