McKean SDEs with singular coefficients

Elena Issoglio (1) , Francesco Russo (2)

1 Dipartimento di Matematica "Giuseppe Peano" [Torino]
2 ENSTA Paris - École Nationale Supérieure de Techniques Avancées

The paper investigates existence and uniqueness for a stochastic differential equation (SDE) with distributional drift depending on the law density of the solution. Those equations are known as McKean SDEs. The McKean SDE is interpreted in the sense of a suitable singular martingale problem. A key tool used in the investigation is the study of the corresponding Fokker-Planck equation.

Mots clés: Stochastic differential equations; distributional drift; McKean; Martingale problem.

Domaines: Probabilités [math.PR]

Elena Issoglio, Francesco Russo. McKean SDEs with singular coefficients. 2021. ⟨hal-03306570v1⟩