Helmholtz theorem for stochastic Hamiltonian systems

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.

References in corpus (3)

• Continuous versus discrete structures I -- Discrete embeddings and ordinary differential equations
• Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions
• Helmholtz theorem for Hamiltonian systems on time scales

Cited by in corpus (2)

• Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions
• Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus