{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:36:35Z","timestamp":1787330195555,"version":"build-2736575974"},"reference-count":15,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2002,1]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1137\/s0036142901395588","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1583-1604","source":"Crossref","is-referenced-by-count":140,"title":["Numerical Methods for Stochastic Systems Preserving Symplectic Structure"],"prefix":"10.1137","volume":"40","author":[{"given":"G. N.","family":"Milstein","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu. M.","family":"Repin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. V.","family":"Tretyakov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0088591"},{"key":"R2","volume-title":"Stochastic differential equations and diffusion processes","author":"Ikeda Nobuyuki","year":"1981"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901387440"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2063-1"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3093-4"},{"key":"R6","volume-title":"Solving ordinary differential equations. I","author":"Hairer E.","year":"1993"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/3\/2\/001"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"J. Sanz\u2010Serna, Symplectic integrators for Hamiltonian problems: an overview, Acta Numer., Cambridge Univ. Press, Cambridge, 1992, 243\u201328693c:65093","DOI":"10.1017\/S0962492900002282"},{"key":"R9","first-page":"78","volume":"2","author":"Suris Yu.","year":"1990","journal-title":"Mat. Model."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8455-5"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12616-5"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994273525"},{"key":"R13","unstructured":"G. N. Milstein, Yu. M. Repin, and M. V. Tretyakov,\n                      Mean\u2010Square Symplectic Methods for Hamiltonian Systems with Multiplicative Noise\n                      , Preprint 670, Weierstra\u00df \u2010Institut f\u00fcr Angewandte Analysis und Stochastik, Berlin, Germany, 2001."},{"key":"R14","first-page":"62","volume":"62","author":"Seeriptsize\u00dfelberg M.","year":"1994","journal-title":"Z. Phys. C","ISSN":"https:\/\/id.crossref.org\/issn\/0170-9739","issn-type":"print"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(94)91295-5"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0036142901395588","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:52:03Z","timestamp":1787327523000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0036142901395588"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["10.1137\/S0036142901395588"],"URL":"https:\/\/doi.org\/10.1137\/s0036142901395588","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,1]]}}}