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This note is sketching a simple and natural mathematical construction forexplaining the probabilistic nature of quantum mechanics. It employsnonstandard analysis and is based on Feynman's interpretation of the Heisenberguncertainty principle, i.e., of the quantum fluctuations, which was brought tothe forefront in some fractal approaches. It results, as in Nelson's stochasticmechanics, in stochastic differential equations which are deduced frominfinitesimal random walks. An extended english abstract gives most of thedetails.

Probabilit\'es et fluctuations quantiques (Probabilities and quantum fluctuations)