Description
Gaussian driven Mckean-Vlasov equation
We study McKean--Vlasov equations driven by Gaussian rough noise. We exploit a regularization effect in the measure variable to transform the equation into one with a time-dependent vector field of complementary Young regularity.
The regularity gain is obtained through Gaussian integration by parts and the Duhamel formula from rough path theory, using the Cameron--Martin structure and the two-dimensional finite variation of the covariance. This yields deterministic stability estimates and an invariance property for the gained regularity. These results provide a pathwise framework for solving distribution-dependent rough equations under irregular Gaussian forcing.