  This paper is a continuation of the study [Chaos.22.033134] of the relation
between the stochastic dynamical systems (DS) and the Witten-type topological
field theories (TFT). Here, it is discussed that stochastic expectation values
of a DS must be complemented on the TFT side by $(-1)^{\hat F}$, where $\hat F$
is the ghost number operator. The role of this inclusion is to unfold the
natural path-integral representation of the TFT, \emph{i.e.}, the Witten index
that equals up to a topological factor to the partition function of the
stochastic noise, into the physical partition function of TFT/DS. It is also
shown that on the DS side, the TFT's wavefunctions are the conditional
probability densities.
