Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111188
Title: Numerical Methods for Stochastic Systems Preserving Symplectic Structure
Authors: Milstein, G. N.
Repin, Yu. M.
Tretyakov, M. V.
Issue Date: 2002
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Citation: Milstein G. N. Numerical Methods for Stochastic Systems Preserving Symplectic Structure / G. N. Milstein, Yu. M. Repin, M. V. Tretyakov // SIAM Journal on Numerical Analysis. — 2002. — Vol. 40. — Iss. 4. — P. 1583-1604.
Abstract: 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.
Keywords: IMPLICIT METHODS
MEAN-SQUARE CONVERGENCE
STOCHASTIC HAMILTONIAN SYSTEMS
SYMPLECTIC INTEGRATION
CONVERGENCE OF NUMERICAL METHODS
DIFFERENTIAL EQUATIONS
FINITE ELEMENT METHOD
HAMILTONIANS
MEAN-SQUARE CONVERGENCE
RANDOM PROCESSES
URI: http://hdl.handle.net/10995/111188
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 0141869053
ISSN: 0036-1429
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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