WIAS Preprint No. 640, (2001)

Symplectic methods for Hamiltonian systems with additive noise


  • Milstein, Grigori N.
  • Repin, Yuri M.
  • Tretyakov, Michael V.

2010 Mathematics Subject Classification

  • 60H10 65C30 65P10


  • Hamiltonian systems with additive noise, symplectic integration, mean-square methods for stochastic differential equations


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.

Appeared in

  • SIAM J. on Numerical Analysis, vol. 39 (2002), no. 6, pp. 2066-2088, under new title: Symplectic integration of Hamiltonian systems with additive noise.

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