An approximation scheme for reflected stochastic differential equations

In this paper, we consider the Stratonovich reflected SDE in a bounded domain . Letting be the N-dyadic piecewise linear interpolation of Wt, we show that the distribution of the solution to the reflected ODE converges weakly to that of (Xt,Lt). Hence, we prove a distributional version for reflected diffusions of the famous result of Wong and Zakai. In particular, we apply our result to derive some geometric properties of coupled reflected Brownian motion, especially those properties which have been used in the recent work on the "hot spots" conjecture for special domains.