# Conversion formula between multidimensional Ito and Stratonovich SDEs

Does anyone on here know of a reference that explicitly computes a conversion formula between the drift terms in multidimensional Ito and Stratonovich SDEs?

In particular, given a solution $(X_t)$ of an N-dimensional Stratonovich SDE $$dX_t=b(X_t)dt+\sigma(X_t)\circ dB_t$$ what is the drift term $\tilde{b}(X_t)$ that makes $(X_t)$ a solution of the Ito SDE $$dX_t=\tilde{b}(X_t)dt+\sigma(X_t)dB_t$$

I've found one online reference so far (http://www.performancetrading.it/Documents/KsStrong/KsS_Conversion.htm), although there is no derivation here and I will not go to the length of actually deriving this myself. I need to cite this result, so a book, paper etc. would be excellent.

P.S.: The conversion formula should be multidimensional. I do of course know the 1-dimensional conversion which is quoted in most standard texts.

Any help is highly appreciated!