Symplectic methods for Hamiltonian systems with additive noise

Abstract

Stochastic systems, phase flows of which have integral invariants, are considered. Hamiltonian systems with additive noise being a wide class of such systems possess the property of preserving symplectic structure. For them, numerical methods preserving the symplectic structure are constructed. A special attention is paid to systems with separable Hamiltonians, to second order differential equations with additive noise, and to Hamiltonian systems with small additive noise

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