Existence and uniqueness for SDEs with irregular drift driven by (fractional) Brownian motion

Abstract: We show that any SDE driven by a Brownian motion with drift satisfying the Krylov-Röckner condition has exactly one solution in an ordinary sense for almost every trajectory of the Brownian motion, i.e. path-by-path uniqueness holds. Furthermore, existence and uniqueness results for SDEs with fractional Brownian noise and distributional drift will be presented. Based on joint work with Khoa Lê and Chengcheng Ling and joint work with Alexandre Richard and Etienne Tanré.