  The quantum hydrodynamic analogy (QHA) equivalent to the Schrodinger equation
is generalized to its stochastic version by a systematic technique. On large
scale, the quantum stochastic hydrodynamic analogy (QSHA) shows dynamics that
under some circumstances may acquire the classical evolution. The QSHA puts in
evidence that in presence of spatially distributed noise the quantum
pseudo-potential restores the quantum behavior on a distance shorter than the
correlation length of fluctuations (named here lc) of the quantum wave function
modulus. The quantum mechanics is achieved in the deterministic limit when lc
tends to infinity with respect to the scale of the problem. When the physical
length of the problem is of order or larger than lc, the quantum potential may
have a finite range of efficacy maintaining the non-local behavior on a
distance lL (named here "quantum non-locality length") depending both by the
noise amplitude and by the inter-particle strength of interaction. In the
deterministic limit (quantum mechanics) the model shows that the "quantum
non-locality length" lLalso becomes infinite. The QSHA unveils that in linear
systems fluctuations are not sufficient to break the quantum non-locality
showing that lL is infinite even if lc is finite.
