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The proposed methods are tested by calculation of Lyapunov exponents and simulation of a laser Langevin equation with multiplicative noises.<\/jats:p>","DOI":"10.1137\/s1064827594278575","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1067-1087","source":"Crossref","is-referenced-by-count":41,"title":["Mean-Square Numerical Methods for Stochastic Differential Equations with Small Noises"],"prefix":"10.1137","volume":"18","author":[{"given":"G. N.","family":"Milstein","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. V.","family":"Tret'yakov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"C. W. Gardiner,\n                      Handbook of Stochastic Methods for Physics, Chemistry and Natural Sciences\n                      , Springer\u2010Verlag, Berlin, 1983."},{"key":"R2","unstructured":"F. Moss and P. V. E. McClintock, eds.\n                      Noise in Nonlinear Dynamical Systems\n                      , Vol. I, II, III, Cambridge University Press, Cambridge, 1989."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/1123045"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/1123045"},{"key":"R4","unstructured":"W. Wagner and E. Platen,\n                      Approximation of Ito Integral Equations\n                      , Zentralinstitut f\u00fcr Mathematik und Mechanik, Akad. der Wiss. der DDR, Berlin, 1978, preprint."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0006577"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0006577"},{"key":"R6","unstructured":"G. N. 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Risken,\n                      The Fokker\u2010Planck Equation\n                      , Springer\u2010Verlag, Berlin, 1984."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.35.1838"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.35.1838"},{"key":"R19","volume":"70","author":"Moss F.","year":"1993","journal-title":"J. Statist. 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