Regularity of Solutions of Mean-Field $G$-SDEs

Karl-Wilhelm Georg Bollweg; Thilo Meyer-Brandis

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arXiv · 2508.07867

Regularity of Solutions of Mean-Field $G$-SDEs

Karl-Wilhelm Georg Bollweg·Thilo Meyer-Brandis

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Abstract

We study regularity properties of the unique solution of a mean-field $G$-SDE. More precisely, we consider a mean-field $G$-SDE with square-integrable random initial condition and establish its first and second order Fr\'echet differentiability in the random initial condition and specify the $G$-SDEs of the respective Fr\'echet derivatives.

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Karl-Wilhelm Georg Bollweg, Thilo Meyer-Brandis. 2025-08-11. Regularity of Solutions of Mean-Field $G$-SDEs. https://arxiv.org/abs/2508.07867

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