Helmholtz theorem for stochastic Hamiltonian systems
Probability
2015-07-23 v1 Optimization and Control
Abstract
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give the associated Hamiltonian. This result show coherence with the approach of \cite{milstein} where the authors answered to this problem through the preservation of the symplectic form but without providing the Hamiltonian associated.
Keywords
Cite
@article{arxiv.1507.06193,
title = {Helmholtz theorem for stochastic Hamiltonian systems},
author = {Frédéric Pierret},
journal= {arXiv preprint arXiv:1507.06193},
year = {2015}
}