Stochastic Hamiltonian dynamical systems
arXiv:math/0702787
Abstract
We use the global stochastic analysis tools introduced by P. A. Meyer and L. Schwartz to write down a stochastic generalization of the Hamilton equations on a Poisson manifold that, for exact symplectic manifolds, are characterized by a natural critical action principle similar to the one encountered in classical mechanics. Several features and examples in relation with the solution semimartingales of these equations are presented.
46 pages. A converse to the Critical Action Principle has been added. The discussion on conserved quantities has been extended and linked to the study of the stability of equilibria of the solution semimartingales