Paracontrolled distributions combine the Fourier techniques of Bony's paradifferential calculus with ideas from the theory of controlled rough paths. This leads to a lightweight calculus for distributions which allows to handle nonlinear operations involving singular objects like white noise, and which allows to give a meaning to and solve singular stochastic (partial) differential equations. I will present the basic ideas and techniques of paracontrolled distributions on a simple model problem.
Based on joint work with Massimiliano Gubinelli and Peter Imkeller.
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