Regularity of Generalized Mean-Field G -SDEs

Karl-Wilhelm Georg Bollweg () and Thilo Meyer-Brandis
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Karl-Wilhelm Georg Bollweg: Department of Mathematics, University of Munich (LMU), 80333 Munich, Germany
Thilo Meyer-Brandis: Department of Mathematics, University of Munich (LMU), 80333 Munich, Germany

Mathematics, 2025, vol. 13, issue 19, 1-40

Abstract: We study the regularity properties of the unique solution of a generalized mean-field G -SDE. More precisely, we consider a generalized mean-field G -SDE with a square-integrable random initial condition, establish its first- and second-order Fréchet differentiability in the stochastic initial condition, and specify the G -SDEs of the respective Fréchet derivatives. The first- and second-order Fréchet derivatives are obtained for locally Lipschitz coefficients admitting locally Lipschitz first- and second-order Fréchet derivatives respectively. Our approach heavily relies on the Grönwall inequality, which leverages the Lipschitz continuity of the coefficients.

Keywords: mean-field; McKean–Vlasov; uncertainty; sublinear expectation; SDEs; derivative; variation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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