Quantum Potential and Random Phase - Space Dynamics
  We analyze limitations upon any kinetic theory inspired derivation of a probabilistic counterpart of the Schr\"{o}dinger picture quantum dynamics. Neither dissipative nor non-dissipative stochastic phase-space processes based on the white-noise (Brownian motion) kinetics are valid candidates unless additional constraints (a suitable form of the energy conservation law) are properly incorporated in the formalism. 
R. Czopnik and P. Garbaczewski