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 ρ-irregularity. As a consequence, we can also treat McKean-Vlasov, transport and continuity equations.

Solution theory of fractional SDEs in complete subcritical regimes

Lucio Galeati;
2025-01-01

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 ρ-irregularity. As a consequence, we can also treat McKean-Vlasov, transport and continuity equations.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/249100
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