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Stochastics and Stochastic Reports Volume 29, 1990 - Issue 2
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Original Articles

An efficient approximation for stochastic differential equations on the partition ofsymmetricalirst

Nigel J. Newton Department of Electronic Systems Engineering, University of Essex, Wivenhoe Park, Colchester, C04 3SQ, UK
Pages 227-258 | Received 21 Feb 1989, Published online: 04 Apr 2007

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Masaaki Fukasawa & Jan Obłój. (2020) Efficient discretisation of stochastic differential equations. Stochastics 92:6, pages 833-851.
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X.Q. Liu & C. W. Li. (1997) Discretization of stochastic differential equations by the product expansion for the chen series. Stochastics and Stochastic Reports 60:1-2, pages 23-40.
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Stamatis Cambams & Hu Yaozhong. (1996) Exact convergence rate of the Euler-Maruyama scheme, with application to sampling design. Stochastics and Stochastic Reports 59:3-4, pages 211-240.
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Articles from other publishers (15)

Bruno Bouchard, Stefan Geiss & Emmanuel Gobet. (2017) First time to exit of a continuous Itô process: General moment estimates and ${\mathrm{L}}_{1}$-convergence rate for discrete time approximations. Bernoulli 23:3.
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Fred Espen Benth, Dan Crisan, Paolo Guasoni, Konstantinos Manolarakis, Johannes Muhle-Karbe, Colm Nee & Philip ProtterD. Crisan, K. Manolarakis & C. Nee. 2013. Paris-Princeton Lectures on Mathematical Finance 2013. Paris-Princeton Lectures on Mathematical Finance 2013 203 316 .
Masaaki Fukasawa. (2011) Discretization error of stochastic integrals. The Annals of Applied Probability 21:4.
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Masaaki Fukasawa. (2010) Realized volatility with stochastic sampling. Stochastic Processes and their Applications 120:6, pages 829-852.
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E. Rapoo. (2016) A Variable Step Size Riemannian Sum for an Itô Integral. Journal of Applied Probability 45:2, pages 551-567.
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E. Rapoo. (2016) A Variable Step Size Riemannian Sum for an Itô Integral. Journal of Applied Probability 45:02, pages 551-567.
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Ziyu Zheng. 2004. Handbook of Computational and Numerical Methods in Finance. Handbook of Computational and Numerical Methods in Finance 403 429 .
Norbert Hofmann, Thomas Müller-Gronbach & Klaus Ritter. (2001) The Optimal Discretization of Stochastic Differential Equations. Journal of Complexity 17:1, pages 117-153.
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Norbert Hofmann, Thomas Müller-Gronbach & Klaus Ritter. (2000) Step size control for the uniform approximation of systems of stochastic differential equations with additive noise. The Annals of Applied Probability 10:2.
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X.Q. Liu & C.W. Li. (1999) Product expansion for stochastic jump diffusions and its application to numerical approximation. Journal of Computational and Applied Mathematics 108:1-2, pages 1-17.
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J. G. Gaines & T. J. Lyons. (1997) Variable Step Size Control in the Numerical Solution of Stochastic Differential Equations. SIAM Journal on Applied Mathematics 57:5, pages 1455-1484.
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Krystyna Twardowska. (1996) Wong-Zakai approximations for stochastic differential equations. Acta Applicandae Mathematicae 43:3, pages 317-359.
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Axel Grorud & Denis Talay. (1996) Approximation of Lyapunov Exponents of Nonlinear Stochastic Differential Equations. SIAM Journal on Applied Mathematics 56:2, pages 627-650.
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Denis Talay. 1995. Probabilistic Methods in Applied Physics. Probabilistic Methods in Applied Physics 54 96 .
Nigel J. Newton. (1991) Asymptotically Efficient Runge-Kutta Methods for a Class of Itô and Stratonovich Equations. SIAM Journal on Applied Mathematics 51:2, pages 542-567.
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