Stochastic Hamiltonian dynamical systems

2007/02/26 by Lázaro-Camí, Joan-Andreu, Ortega, Juan-Pablo · 3 citations
#37Jxx #65Cxx #FOS: Mathematics #Probability (math.PR) #Symplectic Geometry (math.SG)

paper · doi:10.48550/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.

Cited by

• Applications of standard and Hamiltonian stochastic Lie systems
• Persistence of Invariant Tori for Stochastic Nonlinear Schrödinger in the Sense of Most Probable Paths
• A comparative numerical study of stochastic Hamiltonian Camassa-Holm equations

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