{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T22:31:27Z","timestamp":1776205887888,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,9,19]],"date-time":"2016-09-19T00:00:00Z","timestamp":1474243200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"crossref","award":["CRC 701"],"award-info":[{"award-number":["CRC 701"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"crossref","award":["CRC 701"],"award-info":[{"award-number":["CRC 701"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Einstein Center for Mathematics","award":["Matheon A25"],"award-info":[{"award-number":["Matheon A25"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2017,3]]},"DOI":"10.1007\/s10915-016-0290-x","type":"journal-article","created":{"date-parts":[[2016,9,19]],"date-time":"2016-09-19T05:12:06Z","timestamp":1474261926000},"page":"1042-1077","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":54,"title":["Stochastic C-Stability and B-Consistency of Explicit and Implicit Milstein-Type Schemes"],"prefix":"10.1007","volume":"70","author":[{"given":"Wolf-J\u00fcrgen","family":"Beyn","sequence":"first","affiliation":[]},{"given":"Elena","family":"Isaak","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8341-5097","authenticated-orcid":false,"given":"Raphael","family":"Kruse","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,9,19]]},"reference":[{"key":"290_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12878-7","volume-title":"Random Dynamical Systems. Springer Monographs in Mathematics","author":"L Arnold","year":"1998","unstructured":"Arnold, L.: Random Dynamical Systems. Springer Monographs in Mathematics. Springer, Berlin (1998)"},{"issue":"3","key":"290_CR2","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1007\/s10915-015-0114-4","volume":"67","author":"W-J Beyn","year":"2016","unstructured":"Beyn, W.-J., Isaak, E., Kruse, R.: Stochastic C-stability and B-consistency of explicit and implicit Euler-type schemes. J. Sci. Comput. 67(3), 955\u2013987 (2016). doi: 10.1007\/s10915-015-0114-4","journal-title":"J. Sci. Comput."},{"key":"290_CR3","volume-title":"Stability of Runge\u2013Kutta Methods for Stiff Nonlinear Differential Equations, Volume 2 of CWI Monographs","author":"K Dekker","year":"1984","unstructured":"Dekker, K., Verwer, J.: Stability of Runge\u2013Kutta Methods for Stiff Nonlinear Differential Equations, Volume 2 of CWI Monographs. North-Holland, Amsterdam (1984)"},{"issue":"4","key":"290_CR4","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1137\/S0036139992235706","volume":"54","author":"JG Gaines","year":"1994","unstructured":"Gaines, J.G., Lyons, T.J.: Random generation of stochastic area integrals. SIAM J. Appl. Math. 54(4), 1132\u20131146 (1994)","journal-title":"SIAM J. Appl. Math."},{"key":"290_CR5","unstructured":"Gorini, L.: Theorie und Simulation einer zwei-dimensionalen stochastischen Differentialgleichung. B.Sc. thesis, TU Berlin (2015)"},{"key":"290_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-05221-7","volume-title":"Solving Ordinary Differential Equations. II, Volume\u00a014 of Springer Series in Computational Mathematics","author":"E Hairer","year":"1996","unstructured":"Hairer, E., Wanner, G.: Solving Ordinary Differential Equations. II, Volume\u00a014 of Springer Series in Computational Mathematics, 2nd edn. Springer, Berlin (1996). (Stiff and differential-algebraic problems)","edition":"2"},{"issue":"3","key":"290_CR7","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1137\/S0036142901389530","volume":"40","author":"DJ Higham","year":"2002","unstructured":"Higham, D.J., Mao, X., Stuart, A.M.: Strong convergence of Euler-type methods for nonlinear stochastic differential equations. SIAM J. Numer. Anal. 40(3), 1041\u20131063 (2002)","journal-title":"SIAM J. Numer. Anal."},{"issue":"8","key":"290_CR8","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.3934\/dcdsb.2013.18.2083","volume":"18","author":"DJ Higham","year":"2013","unstructured":"Higham, D.J., Mao, X., Szpruch, L.: Convergence, non-negativity and stability of a new Milstein scheme with applications to finance. Discrete Contin. Dyn. Syst. Ser. B 18(8), 2083\u20132100 (2013)","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"issue":"1112","key":"290_CR9","first-page":"99","volume":"236","author":"M Hutzenthaler","year":"2015","unstructured":"Hutzenthaler, M., Jentzen, A.: Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients. Mem. Am. Math. Soc. 236(1112), 99 (2015)","journal-title":"Mem. Am. Math. Soc."},{"issue":"2130","key":"290_CR10","doi-asserted-by":"crossref","first-page":"1563","DOI":"10.1098\/rspa.2010.0348","volume":"467","author":"M Hutzenthaler","year":"2011","unstructured":"Hutzenthaler, M., Jentzen, A., Kloeden, P.E.: Strong and weak divergence in finite time of Euler\u2019s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 467(2130), 1563\u20131576 (2011)","journal-title":"Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci."},{"issue":"4","key":"290_CR11","doi-asserted-by":"crossref","first-page":"1611","DOI":"10.1214\/11-AAP803","volume":"22","author":"M Hutzenthaler","year":"2012","unstructured":"Hutzenthaler, M., Jentzen, A., Kloeden, P.E.: Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Ann. Appl. Probab. 22(4), 1611\u20131641 (2012)","journal-title":"Ann. Appl. Probab."},{"key":"290_CR12","volume-title":"Numerical Solution of Stochastic Differential Equations","author":"PE Kloeden","year":"1999","unstructured":"Kloeden, P.E., Platen, E.: Numerical Solution of Stochastic Differential Equations, 3rd edn. Springer, Berlin (1999)","edition":"3"},{"issue":"1","key":"290_CR13","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s10543-011-0341-5","volume":"52","author":"R Kruse","year":"2012","unstructured":"Kruse, R.: Characterization of bistability for stochastic multistep methods. BIT Numer. Math. 52(1), 109\u2013140 (2012)","journal-title":"BIT Numer. Math."},{"key":"290_CR14","doi-asserted-by":"crossref","unstructured":"Krylov, N.V.: On Kolmogorov\u2019s equation for finite dimensional diffusions. In: Stochastic PDE\u2019s and Kolmogorov Equations in Infinite Dimensions (Cetraro, 1998). Lecture Notes in Math., vol. 1715, pp. 1\u201363. Springer, Berlin (1999)","DOI":"10.1007\/BFb0092417"},{"key":"290_CR15","unstructured":"Kumar, C., Sabanis, S.: On tamed Milstein schemes of SDEs driven by L\u00e9vy noise (2015) (preprint). arXiv:1407.5347v2"},{"key":"290_CR16","unstructured":"Kumar, C., Sabanis, S.: On Milstein approximations with varying coefficients: the case of super-linear diffusion coefficients (2016) (preprint). arXiv:1601.02695"},{"key":"290_CR17","volume-title":"Stochastic Differential Equations and Their Applications","author":"X Mao","year":"1997","unstructured":"Mao, X.: Stochastic Differential Equations and Their Applications. Horwood Publishing Series in Mathematics & Applications, Horwood Publishing Limited, Chichester (1997)"},{"key":"290_CR18","first-page":"583","volume":"19","author":"GN Milstein","year":"1974","unstructured":"Milstein, G.N.: Approximate integration of stochastic differential equations. Teor. Verojatnost. i Primenen. 19, 583\u2013588 (1974). (in Russian)","journal-title":"Teor. Verojatnost. i Primenen."},{"issue":"3","key":"290_CR19","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1137\/1119062","volume":"19","author":"GN Milstein","year":"1975","unstructured":"Milstein, G.N.: Approximate integration of stochastic differential equations. Theory Probab. Appl. 19(3), 557\u2013562 (1975). (translated by K. Durr)","journal-title":"Theory Probab. Appl."},{"key":"290_CR20","volume-title":"Numerical Integration of Stochastic Differential Equations, Volume 313 of Mathematics and its Applications","author":"GN Milstein","year":"1995","unstructured":"Milstein, G.N.: Numerical Integration of Stochastic Differential Equations, Volume 313 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht (1995). (Translated and revised from the 1988 Russian original)"},{"key":"290_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-10063-9","volume-title":"Stochastic Numerics for Mathematical Physics. Scientific Computation","author":"GN Milstein","year":"2004","unstructured":"Milstein, G.N., Tretyakov, M.V.: Stochastic Numerics for Mathematical Physics. Scientific Computation. Springer, Berlin (2004)"},{"key":"290_CR22","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719468","volume-title":"Iterative Solution of Nonlinear Equations in Several Variables, Volume 30 of Classics in Applied Mathematics","author":"JM Ortega","year":"2000","unstructured":"Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables, Volume 30 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2000). (Reprint of the 1970 original)"},{"key":"290_CR23","volume-title":"A Concise Course on Stochastic Partial Differential Equations, Volume 1905 of Lecture Notes in Mathematics","author":"C Pr\u00e9v\u00f4t","year":"2007","unstructured":"Pr\u00e9v\u00f4t, C., R\u00f6ckner, M.: A Concise Course on Stochastic Partial Differential Equations, Volume 1905 of Lecture Notes in Mathematics. Springer, Berlin (2007)"},{"issue":"1","key":"290_CR24","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S0304-4149(00)00053-3","volume":"91","author":"T Ryd\u00e9n","year":"2001","unstructured":"Ryd\u00e9n, T., Wiktorsson, M.: On the simulation of iterated It\u00f4 integrals. Stoch. Process. Appl. 91(1), 151\u2013168 (2001)","journal-title":"Stoch. Process. Appl."},{"key":"290_CR25","doi-asserted-by":"crossref","unstructured":"Strehmel, K., Weiner, R., Podhaisky, H.: Numerik gew\u00f6hnlicher Differentialgleichungen: nichtsteife, steife und differential-algebraische Gleichungen. Studium. Springer Spektrum, Wiesbaden (2012) (2 rev. and ext. edition)","DOI":"10.1007\/978-3-8348-2263-5"},{"key":"290_CR26","volume-title":"Dynamical Systems and Numerical Analysis, Volume 2 of Cambridge Monographs on Applied and Computational Mathematics","author":"AM Stuart","year":"1996","unstructured":"Stuart, A.M., Humphries, A.R.: Dynamical Systems and Numerical Analysis, Volume 2 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge (1996)"},{"issue":"3","key":"290_CR27","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1080\/10236198.2012.656617","volume":"19","author":"X Wang","year":"2013","unstructured":"Wang, X., Gan, S.: The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients. J. Differ. Equ. Appl. 19(3), 466\u2013490 (2013)","journal-title":"J. Differ. Equ. Appl."},{"issue":"2","key":"290_CR28","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1214\/aoap\/1015345301","volume":"11","author":"M Wiktorsson","year":"2001","unstructured":"Wiktorsson, M.: Joint characteristic function and simultaneous simulation of iterated It\u00f4 integrals for multiple independent Brownian motions. Ann. Appl. Probab. 11(2), 470\u2013487 (2001)","journal-title":"Ann. Appl. Probab."},{"key":"290_CR29","unstructured":"Zhang, Z.: New explicit balanced schemes for SDEs with locally Lipschitz coefficients (2014) (preprint). arXiv:1402.3708"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0290-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-016-0290-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0290-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,13]],"date-time":"2019-09-13T14:44:48Z","timestamp":1568385888000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-016-0290-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,19]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,3]]}},"alternative-id":["290"],"URL":"https:\/\/doi.org\/10.1007\/s10915-016-0290-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9,19]]}}}