Stochastic differential equations revisited

Dietrich Ryter

Published 2015-10-05Version 1

The solution of the SDE follows the "trend" of the Fokker-Planck equation, which consists of the drift (given by the SDE) and of a term with derivatives of the diffusion. That extra term must be included in the stochastic integration. This yields the Ito sense of the SDE, while the FPE belongs to the anti-Ito sense and preserves important features of the case with a constant diffusion. An existing inconsistency is thereby removed.