  This note is sketching a simple and natural mathematical construction for
explaining the probabilistic nature of quantum mechanics. It employs
nonstandard analysis and is based on Feynman's interpretation of the Heisenberg
uncertainty principle, i.e., of the quantum fluctuations, which was brought to
the forefront in some fractal approaches. It results, as in Nelson's stochastic
mechanics, in stochastic differential equations which are deduced from
infinitesimal random walks. An extended english abstract gives most of the
details.
