Dynamics and Variational Integrators of Stochastic Hamiltonian Systems

Abstract

Stochastic action integral and Lagrange formalism of stochastic Hamiltonian systems are written through construing the stochastic Hamiltonian systems as nonconservative systems with white noise as the nonconservative 'force'. Stochastic Hamilton's principle and its discrete version are derived. Based on these, a systematic approach of producing symplectic numerical methods for stochastic Hamiltonian systems, i.e., the stochastic variational integrators are established. Numerical tests show validity of this approach.