Non-equilibrium densities of Nelson processes

In this paper we analyze the idea that arbitrary probability densities solutions of the classical evolution equation associated by the Nelson stochastic mechanics to the quantum mechanics always relax in time toward the quantum mechanical density jj derived from the Schrodinger equation The analysis of a few general propositions and of some physical examples show that the choice of the Nelson stochastic ux is correct for a particular class of quantum states but can not be adopted in general This indicates that the question of the time relaxation of the solutions of the Kolmogorov equation associated to a quantum wave function toward the quantum densities is physically meaningful even if a classical probabilistic model good for every quantum state is still not available A few suggestion in this direction are nally discussed