Solution theory of fractional SDEs in complete subcritical regimes

We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with drift coefficient $b$ 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. Furthermore, it has direct consequences for McKean-Vlasov, transport, and continuity equations.Comment: 64 page