High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations, SIAM Journal on Scientific Computing, vol.34, issue.3, pp.1800-1823, 2012. ,
DOI : 10.1137/110846609
URL : https://hal.archives-ouvertes.fr/hal-00746563
Mécanique Aléatoire, Lecture Notes in Mathematics, vol.866, 1981. ,
Stochastic variational integrators, IMA Journal of Numerical Analysis, vol.29, issue.2, pp.421-443, 2009. ,
DOI : 10.1093/imanum/drn018
URL : http://arxiv.org/abs/0708.2187
Low rank Runge???Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise, Journal of Computational and Applied Mathematics, vol.236, issue.16, pp.3920-3930, 2012. ,
DOI : 10.1016/j.cam.2012.03.007
URL : http://dx.doi.org/10.1016/j.cam.2012.03.007
Energy-preserving Runge-Kutta methods, ESAIM: Mathematical Modelling and Numerical Analysis, vol.43, issue.4, pp.645-649, 2009. ,
DOI : 10.1051/m2an/2009020
Linear energy-preserving integrators for??Poisson systems, BIT Numerical Mathematics, vol.41, issue.4, pp.91-101, 2011. ,
DOI : 10.1007/s10543-011-0310-z
Conservative stochastic differential equations: Mathematical and numerical analysis, Mathematics of Computation, vol.78, issue.268, pp.2047-2074, 2009. ,
DOI : 10.1090/S0025-5718-09-02220-0
URL : https://hal.archives-ouvertes.fr/hal-00687269
Time integration and discrete Hamiltonian systems, Journal of Nonlinear Science, vol.115, issue.5, pp.449-467, 1996. ,
DOI : 10.1007/BF02440162
Energy-preserving variant of collocation methods, JNAIAM. J. Numer. Anal. Ind. Appl. Math, vol.5, issue.12, pp.73-84, 2011. ,
Discrete Gradient Approach to Stochastic Differential Equations with a Conserved Quantity, SIAM Journal on Numerical Analysis, vol.49, issue.5, pp.2017-2038, 2011. ,
DOI : 10.1137/090771880
Numerical Solution of Stochastic Differential Equations, Applications of Mathematics, vol.23, 1992. ,
Stochastic hamiltonian dynamical systems, Reports on Mathematical Physics, vol.61, issue.1, pp.65-122, 2008. ,
DOI : 10.1016/S0034-4877(08)80003-1
REDUCTION, RECONSTRUCTION, AND SKEW-PRODUCT DECOMPOSITION OF SYMMETRIC STOCHASTIC DIFFERENTIAL EQUATIONS, Stochastics and Dynamics, vol.09, issue.01, pp.1-46, 2009. ,
DOI : 10.1142/S0219493709002531
Random motion of a rigid body, Journal of Theoretical Probability, vol.10, issue.1, pp.201-211, 1997. ,
DOI : 10.1023/A:1022654717555
Symplectic conditions and stochastic generating functions of stochastic Runge???Kutta methods for stochastic Hamiltonian systems with multiplicative noise, Applied Mathematics and Computation, vol.219, issue.2, pp.635-643, 2012. ,
DOI : 10.1016/j.amc.2012.06.053
Mean-square symplectic methods for Hamiltonian systems with multiplicative noise, 2001. ,
Numerical Methods for Stochastic Systems Preserving Symplectic Structure, SIAM Journal on Numerical Analysis, vol.40, issue.4, pp.1583-1604, 2002. ,
DOI : 10.1137/S0036142901395588
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.598.1816
Conserved quantities and symmetry for stochastic dynamical systems, Physics Letters A, vol.195, issue.3-4, pp.185-189, 1994. ,
DOI : 10.1016/0375-9601(94)90150-3
New conserved quantities derived from symmetry for stochastic dynamical systems, Journal of Physics A: Mathematical and General, vol.27, issue.20, pp.777-782, 1994. ,
DOI : 10.1088/0305-4470/27/20/004
Conserved Quantities and Symmetries Related to Stochastic Dynamical Systems, Annals of the Institute of Statistical Mathematics, vol.51, issue.4, pp.779-802, 1999. ,
DOI : 10.1023/A:1004095516648
Energy conservative stochastic difference scheme for stochastic Hamilton dynamical systems, Japan Journal of Industrial and Applied Mathematics, vol.67, issue.1, pp.119-128, 2000. ,
DOI : 10.1007/BF03167340
Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods, Mathematical Problems in Engineering, vol.23, issue.12, 2010. ,
DOI : 10.1007/BF00773344
URL : http://doi.org/10.1155/2010/384937
Boundary Preserving Semianalytic Numerical Algorithms for Stochastic Differential Equations, SIAM Journal on Scientific Computing, vol.29, issue.4, pp.1525-1549, 2007. ,
DOI : 10.1137/05063725X
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.259.9437
Zur zeitdiskreten approximation von Itoprozessen, Diss. B. Imath. Akad. des Wiss. der DDR, 1984. ,
A new class of energy-preserving numerical integration methods, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.4, p.45206, 2008. ,
DOI : 10.1088/1751-8113/41/4/045206
Dynamics and variational integrators of stochastic Hamiltonian systems, Int. J. Numer. Anal. Model, vol.6, issue.4, pp.586-602, 2009. ,
Variational Integrators and Generating Functions for Stochastic Hamiltonian Systems, 2007. ,