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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!

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Here is a reference for the multidimensional Itô-Stratonovich conversion: pages 137 and 138 of Theory and Numerics of Differential Equations, by James Blowey, John P. Coleman, Alan W. Craig (Springer, 2013).

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