New forward equation for stochastic differential equations with multiplicative noise

Dietrich Ryter

Published 2019-07-02Version 1

The existing forward equation defines a probability current that disagrees with the random paths. A new one is adequate. With respect to that, the existing Ito paths consist of most probable increments (rather than mean ones), with Gaussian deviations. Further new features are the compliance with prediction theory and the agreement with physical steady states. Multiplicative noise, in particular the "spurious drift", does no longer show up in the relevant equations.