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Numerical Methods for Stochastic Systems Preserving Symplectic Structure
Stochastic Hamiltonian systems with multiplicative noise, phase flows of which preserve symplectic structure, are considered. To construct symplectic methods for such systems, sufficiently general fully implicit schemes, i.e., schemes with implicitness both in deterministic and stochastic terms, are...
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| Published in: | SIAM journal on numerical analysis 2002-01, Vol.40 (4), p.1583-1604 |
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| Main Authors: | , , |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c313t-b5b44c920d2ff56a10e9cef2146865192c492b99b307ecf7de791823c0331d3f3 |
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| container_title | SIAM journal on numerical analysis |
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| creator | Milstein, G. N. Repin, Yu. M. Tretyakov, M. V. |
| description | Stochastic Hamiltonian systems with multiplicative noise, phase flows of which preserve symplectic structure, are considered. To construct symplectic methods for such systems, sufficiently general fully implicit schemes, i.e., schemes with implicitness both in deterministic and stochastic terms, are needed. A new class of fully implicit methods for stochastic systems is proposed. Increments of Wiener processes in these fully implicit schemes are substituted by some truncated random variables. A number of symplectic integrators is constructed. Special attention is paid to systems with separable Hamiltonians. Some results of numerical experiments are presented. They demonstrate superiority of the proposed symplectic methods over very long times in comparison with nonsymplectic ones. |
| doi_str_mv | 10.1137/S0036142901395588 |
| format | article |
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| ispartof | SIAM journal on numerical analysis, 2002-01, Vol.40 (4), p.1583-1604 |
| issn | 0036-1429 1095-7170 |
| language | eng |
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| source | SIAM Journals Archive; ABI/INFORM Collection; JSTOR Archival Journals and Primary Sources Collection |
| subjects | Applied mathematics Approximation Methods Noise Numerical analysis Random variables |
| title | Numerical Methods for Stochastic Systems Preserving Symplectic Structure |
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