Properties of the Flows Generated by Stochastic Equations with Reflection

We consider the 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 from the boundary that starts from a point x. We characterize inner and boundary points of the set ϕ _t (ℝ ₊ ^d ) and prove that the Hausdorff dimension of the boundary ∂ϕ _t (ℝ ₊ ^d ) does not exceed d − 1. __________ Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1069 – 1078, August, 2005.