  Given a domain G, a reflection vector field d(.) on the boundary of G, and
drift and dispersion coefficients b(.) and \sigma(.), let L be the usual
second-order elliptic operator associated with b(.) and \sigma(.). Under
suitable assumptions that, in particular, ensure that the associated
submartingale problem is well posed, it is shown that a probability measure
$\pi$ on \bar{G} is a stationary distribution for the corresponding reflected
diffusion if and only if $\pi (\partial G) = 0$ and $\int_{\bar{G}} L f (x) \pi
(dx) \leq 0$ for every f in a certain class of test functions. Moreover, the
assumptions are shown to be satisfied by a large class of reflected diffusions
in piecewise smooth multi-dimensional domains with possibly oblique reflection.
