BRST gauge fixing procedure applied to SDEs leads directly to the Witten index. The Witten index is of topological character and it does not respond to any perturbation. In particular, all response correlators calculated using the Witten index vanish. This fact has a physical interpretation within the STS: the physical meaning of the Witten index is the partition function of the noise and since there is no backaction from the dynamical system to the noise, the Witten index has no information on the details of the SDE. In contrast, the information on the details of the model is contained in the other trace-like object of the theory, the dynamical partition function, Z t t ′ = ∫ ∫ … … ∫ ∫ a . p . b . c . e ( Q , Ψ Ψ ) D Φ Φ = Tr ⁡ ⁡ M ^ ^ t t ′ , where a.p.b.c. denotes antiperiodic boundary conditions for the fermionic fields and periodic boundary conditions for bosonic fields. In the standard manner, the dynamical partition function can be promoted to the generating functional by coupling the model to external probing fields.