Stochastic Hamiltonian dynamical systems

Details Stochastic Hamiltonian dynamical systems Stochastic Hamiltonian dynamical systems

2007-02-26

arxiv.org/abs/math/0702787v3

Mathematics

Probability

46 pages. A converse to the Critical Action Principle has been added. The discussion on conserved quantities has been extended

Scientific paper

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.

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