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!



Conversion formula between multidimensional Ito and Stratonovich SDEs
Here is a reference for the multidimensional Itô-Stratonovich conversion: [pages 137 and 138](https://books.google.nl/books?id=_WfwCAAAQBAJ&pg=PA137&lpg=PA137) of *Theory and Numerics of Differential Equations*, by James Blowey, John P. Coleman, Alan W. Craig (Springer, 2013).


