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Stochastics and Stochastic Reports Volume 59, 1996 - Issue 3-4
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Original Articles

Exact convergence rate of the Euler-Maruyama scheme, with application to sampling design

Stamatis Cambams Center of Stochastic Processes, Department of Statistics, The University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599-3260
&
Hu Yaozhong Center of Stochastic Processes, Department of Statistics, The University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599-3260
Pages 211-240 | 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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Yaozhong Hu. (2000) Optimal times to observe in the kalman-bucy models. Stochastics and Stochastic Reports 69:1-2, pages 123-140.
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Articles from other publishers (20)

Simon Hatzesberger. (2020) Strongly asymptotically optimal schemes for the strong approximation of stochastic differential equations with respect to the supremum error. Journal of Complexity 60, pages 101496.
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Mario Hefter, André Herzwurm & Thomas Müller-Gronbach. (2019) Lower error bounds for strong approximation of scalar SDEs with non-Lipschitzian coefficients. The Annals of Applied Probability 29:1.
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Lukas Merten, Chad Bustard, Ellen G. Zweibel & Julia Becker Tjus. (2018) The Propagation of Cosmic Rays from the Galactic Wind Termination Shock: Back to the Galaxy?. The Astrophysical Journal 859:1, pages 63.
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Yaozhong Hu, Yanghui Liu & David Nualart. (2016) Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions. The Annals of Applied Probability 26:2.
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Martin Hairer, Martin Hutzenthaler & Arnulf Jentzen. (2015) Loss of regularity for Kolmogorov equations. The Annals of Probability 43:2.
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Henri Schurz. 2012. Stochastic Differential Equations and Processes. Stochastic Differential Equations and Processes 1 139 .
Masaaki Fukasawa. (2011) Discretization error of stochastic integrals. The Annals of Applied Probability 21:4.
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Benjamin Jourdain & Arturo Kohatsu-Higa. 2011. Stochastic Analysis with Financial Applications. Stochastic Analysis with Financial Applications 121 144 .
Andreas Neuenkirch. (2008) Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion. Stochastic Processes and their Applications 118:12, pages 2294-2333.
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Thomas Müller-Gronbach & Klaus Ritter. 2008. Monte Carlo and Quasi-Monte Carlo Methods 2006. Monte Carlo and Quasi-Monte Carlo Methods 2006 53 82 .
Thomas Müller-Gronbach, Klaus Ritter & Tim Wagner. 2008. Monte Carlo and Quasi-Monte Carlo Methods 2006. Monte Carlo and Quasi-Monte Carlo Methods 2006 577 589 .
Andreas Neuenkirch & Ivan Nourdin. (2007) Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion. Journal of Theoretical Probability 20:4, pages 871-899.
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Thomas Müller-Gronbach & Klaus Ritter. (2007) An implicit Euler scheme with non-uniform time discretization for heat equations with multiplicative noise. BIT Numerical Mathematics 47:2, pages 393-418.
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Andreas Neuenkirch. (2006) Optimal approximation of SDE's with additive fractional noise. Journal of Complexity 22:4, pages 459-474.
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Thomas Müller-Gronbach. (2004) Optimal pointwise approximation of SDEs based on Brownian motion at discrete points. The Annals of Applied Probability 14:4.
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Yaozhong Hu, Salah-Eldin A. Mohammed & Feng Yan. (2004) Discrete-time approximations of stochastic delay equations: The Milstein scheme. The Annals of Probability 32:1A.
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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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Yaozhong Hu. (2000) MULTI-DIMENSIONAL GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE. Acta Mathematica Scientia 20:3, pages 341-358.
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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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Eckhard Platen. (2008) An introduction to numerical methods for stochastic differential equations. Acta Numerica 8, pages 197-246.
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