Approche intrinsèque des fluctuations browniennes en mécanique stochastique

Michel Fliess (1, 2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 ALIEN - Algebra for Digital Identification and Estimation

This Note is answering an old questioning about the Fényes-Nelson stochastic mechanics. Feynman's interpretation of the Heisenberg uncertainty principle allows to deduce the Brownian fluctuations, which are associated to this mechanics, from an infinitesimal time-discretisation stemming from non-standard analysis. It is therefore no more necessary to combine those fluctuations with a background field, which has never been well understood. Let us add that an extended english abstract is giving most of the details.

Mots clés: Stochastic mechanics; quantum mechanics; nonstandard analysis; probability; stochastic differential equations; diffusions

Domaines: Logique [math.LO]; Optimisation et contrôle [math.OC]; Probabilités [math.PR]; Physique Quantique [quant-ph]

Michel Fliess. Approche intrinsèque des fluctuations browniennes en mécanique stochastique. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2006. ⟨inria-00081461⟩