The finite-time SEO can be obtained in another, more mathematical way based on the idea to study the SDE-induced actions on differential forms directly, without going through the BRST gauge fixing procedure. The so-obtained finite-time SEO is known in dynamical systems theory as the generalized transfer operator and it has also been used in the classical theory of SDEs (see, e.g., Refs. ). The contribution to this construction from STS is the exposition of the supersymmetric structure underlying it and establishing its relation to the BRST procedure for SDEs.