The Stratonovich SDE:
f or i = 1, ..., N ; j = 1, ..., M
with the same solutions as the N-dimensional Ito SDE with an M-dimensional Wiener process:
has a drift coefficient that is defined given a component-wise by:
whereas a given a is defined component-wise by:
These are called the drift correction formulas. Note that the diffusion coef-
ficients are the same in both the Ito and Stratonovich SDEs.
Prof. Klaus Schmitz