[A stochastic Noether theorem]
In the framework of the stochastic embedding of Lagrangian systems, we define a calculus of variations on stochastic processes. We prove a Noether theorem based on stochastic suspensions of one-parameter groups of diffeomorphisms.
Dans le cadre du plongement stochastique des systèmes lagrangiens, on définit un calcul des variations sur les processus. On démontre un théorème de Noether basé sur la notion de suspension stochastique d'un groupe à un paramètre de difféomorphismes.
Accepted:
Published online:
Jacky Cresson 1; Sébastien Darses 2
@article{CRMATH_2007__344_4_259_0, author = {Jacky Cresson and S\'ebastien Darses}, title = {Th\'eor\`eme de {Noether} stochastique}, journal = {Comptes Rendus. Math\'ematique}, pages = {259--264}, publisher = {Elsevier}, volume = {344}, number = {4}, year = {2007}, doi = {10.1016/j.crma.2006.12.017}, language = {fr}, }
Jacky Cresson; Sébastien Darses. Théorème de Noether stochastique. Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 259-264. doi : 10.1016/j.crma.2006.12.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.12.017/
[1] Mathematical Methods of Classical Mechanics, Springer, 1989
[2] J. Cresson, S. Darses, Stochastic embedding of dynamical systems, Prépublication de l'I.H.É.S. 06/27, 2006, 87 p
[3] Plongement stochastique des systèmes lagrangiens, C. R. Acad. Sci. Paris, Ser. I, Volume 342 (2006), pp. 333-336
[4] Integration by parts and time reversal for diffusion processes, Ann. Probab., Volume 17 (1989) no. 1, pp. 208-238
[5] Dynamical Theories of Brownian Motion, Princeton University Press, 2001
[6] The Malliavin Calculus and Related Topics, Springer-Verlag, 1996
[7] Probability and quantum symmetries I. The theorem of Noether in Schrödinger 's euclidean mechanics, Ann. Inst. H. Poincaré Phys. Théor., Volume 67 (1997) no. 3, pp. 297-338
[8] Quelques résultats de “mécanique stochastique”, Séminaire de Probabilités, Volume XVIII (1982/83), pp. 223-244
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