Mean-field stochastic differential equations driven by <inline-formula><tex-math id="M1">$ G $</tex-math></inline-formula>-Brownian motion

Abstract

The main purpose of this paper is to analyze the mean-field stochastic differential equations driven by $ G $-Brownian motion (mean-field $ G $-SDEs). We first investigate the existence and uniqueness of the solution for the mean-field $ G $-SDEs by utilizing the Banach fixed point theorem. Moreover, by the method of coupling by change of measures, the Harnack and log-Harnack inequalities for mean-field $ G $-SDEs with additive noise are established.