Properties of the Flows Generated by Stochastic Equations with Reflection - Pilipenko, A. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
We consider properties of a random set φ_t(R_+^d), where φ_t(x) is a solution of a stochastic differential equation in R_+^d with normal reflection on the boundary starting at the point x. We perform the characterization of inner and boundary points of the set φ_t(R_+^d). We prove that the Hausdorff dimension of the boundary φ_t(R_+^d) is not greater than d - 1.