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Regularity of Generalized Mean-Field G -SDEs

Author

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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)

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.

Suggested Citation

  • Karl-Wilhelm Georg Bollweg & Thilo Meyer-Brandis, 2025. "Regularity of Generalized Mean-Field G -SDEs," Mathematics, MDPI, vol. 13(19), pages 1-40, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:19:p:3099-:d:1759620
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