On a decomposition of symmetric diffusions with reflecting boundary conditions

We consider a symmetric diffusion corresponding to uniformly elliptic divergence form operator with reflection at the boundary of a domain satisfying the general conditions introduced by Lions and Sznitman. We prove that for each starting point inside the domain the diffusion is a Dirichlet process in the sense of Föllmer and we obtain the Lyons–Zheng–Skorokhod representation of its zero quadratic variation part.