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Volume 6, Issue 4
Dynamics and Variational Integrators of Stochastic Hamiltonian Systems

L. Wang, J. Hong, R. Scherer & F. Bai

Int. J. Numer. Anal. Mod., 6 (2009), pp. 586-602.

Published online: 2009-06

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  • Abstract

Stochastic action integral and Lagrange formalism of stochastic Hamiltonian systems are written through construing the stochastic Hamiltonian systems as nonconservative systems with white noise as the nonconservative 'force'. Stochastic Hamilton's principle and its discrete version are derived. Based on these, a systematic approach of producing symplectic numerical methods for stochastic Hamiltonian systems, i.e., the stochastic variational integrators are established. Numerical tests show validity of this approach.

  • Keywords

Hamilton's principle, stochastic Hamiltonian systems, symplectic methods, variational integrators.

  • AMS Subject Headings

65H10, 65C30, 65P10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-586, author = {L. Wang, J. Hong, R. Scherer and F. Bai}, title = {Dynamics and Variational Integrators of Stochastic Hamiltonian Systems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {4}, pages = {586--602}, abstract = {

Stochastic action integral and Lagrange formalism of stochastic Hamiltonian systems are written through construing the stochastic Hamiltonian systems as nonconservative systems with white noise as the nonconservative 'force'. Stochastic Hamilton's principle and its discrete version are derived. Based on these, a systematic approach of producing symplectic numerical methods for stochastic Hamiltonian systems, i.e., the stochastic variational integrators are established. Numerical tests show validity of this approach.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/785.html} }
TY - JOUR T1 - Dynamics and Variational Integrators of Stochastic Hamiltonian Systems AU - L. Wang, J. Hong, R. Scherer & F. Bai JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 586 EP - 602 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/785.html KW - Hamilton's principle, stochastic Hamiltonian systems, symplectic methods, variational integrators. AB -

Stochastic action integral and Lagrange formalism of stochastic Hamiltonian systems are written through construing the stochastic Hamiltonian systems as nonconservative systems with white noise as the nonconservative 'force'. Stochastic Hamilton's principle and its discrete version are derived. Based on these, a systematic approach of producing symplectic numerical methods for stochastic Hamiltonian systems, i.e., the stochastic variational integrators are established. Numerical tests show validity of this approach.

L. Wang, J. Hong, R. Scherer and F. Bai. (2009). Dynamics and Variational Integrators of Stochastic Hamiltonian Systems. International Journal of Numerical Analysis and Modeling. 6 (4). 586-602. doi:
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