Geodesic
Weak symplectic schemes for stochastic Hamiltonian equations
Electronic transactions on numerical analysis, Tome 43 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We propose a systematic approach to construct symplectic schemes in the weak sense for stochastic Hamiltonian systems. This method is based on generating functions, so it is an extension of the techniques used for constructing high-order symplectic schemes for deterministic Hamiltonian systems. Although the developed symplectic schemes are implicit, they are comparable with the explicit weak Taylor schemes in terms of the number and the complexity of the multiple Itô stochastic integrals required. We study the convergence of the proposed symplectic weak order 2 schemes. The excellent long term performance of the symplectic schemes is verified numerically.
Classification : 65C30, 65P10, 60H10
Keywords: stochastic Hamiltonian systems, symplectic integration, numerical scheme in weak sense 
@article{ETNA_2015__43__a11,
     author = {Anton, Cristina and Deng, Jian and Wong, Yau Shu},
     title = {Weak symplectic schemes for stochastic {Hamiltonian} equations},
     journal = {Electronic transactions on numerical analysis},
     publisher = {mathdoc},
     volume = {43},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__43__a11/}
}
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Anton, Cristina; Deng, Jian; Wong, Yau Shu. Weak symplectic schemes for stochastic Hamiltonian equations. Electronic transactions on numerical analysis, Tome 43 (2015). http://geodesic.mathdoc.fr/item/ETNA_2015__43__a11/