Stochastic flows with reflection

Some topological properties of stochastic flow ${\phi }_t(x)$ generated by stochastic differential equation in a ${\mathbb{R}}_{+}^d$ with normal reflection at the boundary are investigated. Sobolev differentiability in initial condition is received. The absolute continuity of the measure-valued process $\mu \circ {\phi }_t^{-1}$, where $\mu \ll {\lambda }^d,$ is studied.