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