Isovecteurs pour l'équation de Hamilton–Jacobi–Bellman,différentielles stochastiques formelles et intégrales premières en mécanique quantique euclidienne

We give a stochastic interpretation of the geometrical representation, from E. Cartan, of the heat equation, in terms of ideal exterior differential forms and isovectors generating the symmetries of this equation. The method can also be used to interpret as a stochastic deformation the contact geometry of first order ordinary differential equations and the search for infinitesimal symmetries of the associated Hamilton–Jacobi equation. We thus generalise, in an elegant and geometrical way, the results coming originally from long calculations of stochastic analysis. To cite this article: P. Lescot, J.-C. Zambrini, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 263–266.