A Theorem on the Order of Convergence of Mean-Square Approximations of Solutions of Systems of Stochastic Differential Equations

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Previous article Next article A Theorem on the Order of Convergence of Mean-Square Approximations of Solutions of Systems of Stochastic Differential EquationsG. N. Mil–shteinG. N. Mil–shteinhttps://doi.org/10.1137/1132113PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. I. Gikhman and , A. V. Skorokhod, Stochastic Differential Equations, Springer-Verlag, Berlin, New York, 1972 0242.60003 CrossrefGoogle Scholar[2] G. N. Mil'shtein, Approximate integration of stochastic differential equations, Theory Probab. Appl., 19 (1974), 557–563 10.1137/1119062 LinkGoogle Scholar[3] E. Platen, An approximation method for a class of Itô processes, Litovsk. Mat. Sb., 21 (1981), 121–133, (In Russian.) 82g:60083 0465.60055 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Uniformly accurate schemes for drift–oscillatory stochastic differential equationsApplied Numerical Mathematics, Vol. 181 Cross Ref A splitting method for SDEs with locally Lipschitz drift: Illustration on the FitzHugh-Nagumo modelApplied Numerical Mathematics, Vol. 179 Cross Ref Curved schemes for stochastic differential equations on, or near, manifolds29 June 2022 | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 478, No. 2262 Cross Ref Qualitative properties of different numerical methods for the inhomogeneous geometric Brownian motionJournal of Computational and Applied Mathematics, Vol. 406 Cross Ref Split-step double balanced approximation methods for stiff stochastic differential equations7 June 2018 | International Journal of Computer Mathematics, Vol. 96, No. 5 Cross Ref Algebraic structures and stochastic differential equations driven by Lévy processes23 January 2019 | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475, No. 2221 Cross Ref An improved Milstein method for stiff stochastic differential equations1 December 2015 | Advances in Difference Equations, Vol. 2015, No. 1 Cross Ref An error corrected Euler–Maruyama method for stiff stochastic differential equationsApplied Mathematics and Computation, Vol. 256 Cross Ref On the numerical stability of simulation methods for SDEs under multiplicative noise in financeQuantitative Finance, Vol. 13, No. 2 Cross Ref A class of split-step balanced methods for stiff stochastic differential equations19 January 2012 | Numerical Algorithms, Vol. 61, No. 1 Cross Ref Numerical Solution of Stochastic Differential Equations in Finance10 July 2011 Cross Ref Basic Concepts of Numerical Analysis of Stochastic Differential Equations Explained by Balanced Implicit Theta Methods18 August 2011 Cross Ref A Second-Order Strong Method for the Langevin Equations with Holonomic ConstraintsBakytzhan Kallemov and Gregory H. 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