Rough nonlocal diffusions

Abstract

We consider a nonlinear Fokker–Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean–Vlasov diffusion with “common” noise. To study the equation we build a self-contained framework of non-linear rough integration theory which we use to study McKean–Vlasov equations perturbed by rough paths. We construct an appropriate notion of solution of the corresponding Fokker–Planck equation and prove well-posedness.