Existence and Regularity of Solutions to Multi-Dimensional Mean-Field Stochastic Differential Equations with Irregular Drift

Abstract

We examine existence and uniqueness of strong solutions of multi-dimensional mean-field stochastic differential equations with irregular drift coefficients. Furthermore, we establish Malliavin differentiability of the solution and show regularity properties such as Sobolev differentiability in the initial data as well as Hölder continuity in time and the initial data. Using the Malliavin and Sobolev differentiability we formulate a Bismut-Elworthy-Li type formula for mean-field stochastic differential equations, i.e. a probabilistic representation of the first order derivative of an expectation functional with respect to the initial condition.

References in corpus (2)

• Mean-field backward stochastic differential equations: A limit approach
• Nonlinear SDEs driven by Lévy processes and related PDEs

Cited by in corpus (2)

• McKean-Vlasov equations on infinite-dimensional Hilbert spaces with irregular drift and additive fractional noise
• Strong Solutions of Mean-Field SDEs with irregular expectation functional in the drift