In "On the Gap Between Deterministic and Stochastic Ordinary Differential Equations," The Annals of Probability, Vol. 6, No. 1 (Feb., 1978), pp. 19-41, Hector J. Sussmann showed that a stochastic differential equation can be solved by simply solving, for each sample path of the process, the corresponding non stochastic ordinary differential equation, and that for the particular case of a Wiener process, the solution obtained turns out to be the solution in the sense of Stratonovich.
The paper observes that the results are not valid for equations with several stochastic inputs, because of commutativity issues. My question is: has the problem been solved for the multi-input case? Do comparable results exist?