I am currently involved in some understanding on this matter with a colleague of mine. I know all the literature about but I do not know the state of art. Please, could you provide some relevant recent literature about? Also explanations are much appreciated.
My present view is that there exists a time scale that defines the limit of validity of a Chapman-Kolmogorov like equation. It is a situation very similar to quantum chaos but I do not know if this has been currently caught.