2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163569We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position. The derivative is a linear map represented by a multiplicative functional for reflected Brownian motion. The method of proof is based on excursion theory and analysis of the deterministic Skorokhod equation.Probability60J65; 60J50text