Stochastic sewing lemma with propagators and uniqueness of solutions of stochastic heat equation with distributional drift

(Joint work with Siva Athreya, Khoa Le and Leonid Mytnik)

A standard technique for showing existence and uniqueness of solutions of SDEs with irregular drift is the Zvonkin transformation. Unfortunately, for SPDEs due to the lack of Ito’s formula this method does not work.

In the talk I will present a new approach to studying SPDEs with irregular drift, which is inspired by the stochastic sewing lemma (SSL) of Le (2018). We develop a new version of SSL, which is suitable for SPDEs and show existence and uniqueness of solutions to the stochastic heat equation with the distributional drift.