  In this paper we consider the Stratonovich reflected stochastic differential
equation $dX_t=\sigma(X_t)\circ dW_t+b(X_t)dt+dL_t$ in a bounded domain $\O$
which satisfies conditions, introduced by Lions and Sznitman, which are
specified below. Letting $W^N_t$ be the $N$-dyadic piecewise linear
interpolation of $W_t$ what we show is that one can solve the reflected
ordinary differential equation $\dot X^N_t=\sigma(X^N_t)\dot
W^N_t+b(X^N_t)+\dot L^N_t$ and that the distribution of the pair
$(X^N_t,L^N_t)$ converges weakly to that of $(X_t,L_t)$. Hence, what we prove
is a distributional version for reflected diffusions of the famous result of
Wong and Zakai. Perhaps the most valuable contribution made by our procedure
derives from the representation of $\dot X^N_t$ in terms of a projection of
$\dot W_t^N$. In particular, we apply our result in hand to derive some
geometric properties of coupled reflected Brownian motion in certain domains,
especially those properties which have been used in recent work on the "hot
spots" conjecture for special domain.
