Somewhat old paper, https://arxiv.org/abs/1506.04696. I recently spent some time going over this, and the paper has some great proofs and discussion. I did however,find myself looking at their theorem and thinking “how on earth did they find that form of the drift coefficient”, and found the proof to be mainly about showing if you use that form, the result holds. That’s not too enlightening if you want insight into how they found the result, so I went the other way myself, and in 1D it turns out to be somewhat straight-forward. I wrote it up if anybody else finds this view interesting

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https://chrisorm.github.io/SDE-S.html