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@ChrisRackauckas thank you so much for this unexpected feedback and for the reference; this method sounded too good to be true but I have not verified its claims in practice. I haven't been studying this field for a few months and missed this very informative rebuttal.
See Wilkie, Numerical Methods for Stochastic Differential Equations ( https://arxiv.org/pdf/quant-ph/0407039.pdf ) and Kloeden, Platen, Numerical solution of SPDEs
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