It is shown that the Bohm equations for the phase $S$ and squared modulus $\rho$ of the quantum mechanical wave function can be derived from the classical ensemble equations admiting an aditional momentum $p_s$ of the form proportional to the osmotic velocity in the Nelson stochastic mechanics and using the variational principle with appropriate change of variables. The possibility to treat grad$S$ and $p_s$ as two parts of the momentum of quantum ensemble particles is considered from the view point of uncertainty relations of Robertson - Schrödinger type on the examples of the stochastic image of quantum mechanical canonical coherent and squeezed states.
Dimitar A. Trifonov. Blagovest A. Nikolov. Ivaïlo M. Mladenov. "On the Uncertainty Relations in Stochastic Mechanics." J. Geom. Symmetry Phys. 16 57 - 75, 2009. https://doi.org/10.7546/jgsp-16-2009-57-75