A Wong-Zakai theorem for SDEs with singular drift

We study stochastic differential equations (SDEs) with multiplicative Stratonovich-type noise of the form $ dX_t = b(X_t) dt + \sigma(X_t)\circ d W_t, X_0=x_0\in$\mathbb{R}$^d, t\geq0,$withapossiblysingulardrift$b\in L^{{p}}($\mathbb{R}$^d)$,$p>d$and$p\geq 2$, and show that such SDEs can be approximated by random ordinary differential equations by smoothing the noise and the singular drift at the same time. We further prove a support theorem for this class of SDEs in a rather simple way using the Girsanov theorem.