Mean-field stochastic differential equations driven by G-Brownian motion

Abstract

This paper introduces a novel formulation of mean-field stochastic differential equations driven by G-Brownian motion. The proposed formulation generalises existing approaches within the G-framework and enables the study of Fréchet differentiability. Under non-Lipschitz conditions on the coefficients, we establish the existence and uniqueness of a solution for square-integrable stochastic initial data.

Keywords

Mean-field stochastic differential equations / G-Brownian motion / G-framework / Fréchet differentiability / Existence and uniqueness of a solution

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