  The recent analysis on noncommutative geometry, showing quantization of the
volume for the Riemannian manifold entering the geometry, can support a view of
quantum mechanics as arising by a stochastic process on it. A class of
stochastic processes can be devised, arising as fractional powers of an
ordinary Wiener process, that reproduce in a proper way a stochastic process on
a noncommutative geometry. These processes are characterized by producing
complex values and so, the corresponding Fokker-Planck equation resembles the
Schroedinger equation. Indeed, by a direct numerical check, one can recover the
kernel of the Schroedinger equation starting by an ordinary Brownian motion.
This class of stochastic processes needs a Clifford algebra to exist. In four
dimensions, the full set of Dirac matrices is needed and the corresponding
stochastic process in a noncommutative geometry is easily recovered as is the
Dirac equation in the Klein-Gordon form being it the Fokker--Planck equation of
the process.
