A probabilistic deformation of calculus of variations with constraints

Christian Léonard (1) , Jean-Claude Zambrini (2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 GFMUL - Grupo de Fisica Matematica

In the framework of a probabilistic deformation of the classical calculus of variations, we consider the simplest problem of constraints, and solve it in two different ways. First by a pathwise argument in the line of Euclidean Quantum Mechanics. Second from an entropic (measure theoretic) perspective.

Mots clés: Probabilistic calculus of variations; Stochastic least action principle; Conditional law of large numbers; Relative entropy; Bernstein processes

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]

Christian Léonard, Jean-Claude Zambrini. A probabilistic deformation of calculus of variations with constraints. Seminar on stochastic analysis, random fields and applications, VI, 2008, Ascona, Switzerland. pp.177-189. ⟨hal-00515417⟩