  We prove the unique solvability in weighted Sobolev spaces of non-divergence
form elliptic and parabolic equations on a half space with the homogeneous
Neumann boundary condition. All the leading coefficients are assumed to be only
measurable in the time variable and have small mean oscillations in the spatial
variables. Our results can be applied to Neumann boundary value problems for
{\em stochastic} partial differential equations with BMO$_x$ coefficients.
