Partial and full solutions of stochastic differential equations

Abstract

Only the "anti-Ito" integral yields the correct shift of the mean, by the fact that the elements of its Riemannian sum hold in the order O(dt) rather than only in O(sqrt dt). The corresponding "full" Fokker-Planck equation is particularly simple and the only one applying for Brownian motion with an arbitrary friction law. The "full" backward equation coincides with it in the noise contribution.