Solution theory of fractional SDEs in complete subcritical regimes

Abstract

We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that includes strong existence, path-by-path uniqueness, existence of a solution flow of diffeomorphisms, Malliavin differentiability and $\rho$-irregularity. As a consequence, we can also treat McKean-Vlasov, transport and continuity equations.