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May 2000 Step size control for the uniform approximation of systems of stochastic differential equations with additive noise
Norbert Hofmann, Thomas Müller-Gronbach, Klaus Ritter
Ann. Appl. Probab. 10(2): 616-633 (May 2000). DOI: 10.1214/aoap/1019487358

Abstract

We analyze the pathwise approximation for systems of stochastic differential equations.The pathwise distance between the solution and its approximation is measured globally on the unit interval in the $L_{\infty}$-norm, and we study the expectation of this distance. For systems with additive noise we obtain sharp lower and upper bounds for the minimal error in the class of arbitrary methods which use discrete observations of a Brownian path. The optimal order is achieved by an Euler scheme with adaptive step-size control. We illustrate the superiority of the adaptive method compared to equidistant discretization by a simulation experiment.

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Norbert Hofmann. Thomas Müller-Gronbach. Klaus Ritter. "Step size control for the uniform approximation of systems of stochastic differential equations with additive noise." Ann. Appl. Probab. 10 (2) 616 - 633, May 2000. https://doi.org/10.1214/aoap/1019487358

Information

Published: May 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1054.65007
MathSciNet: MR1768220
Digital Object Identifier: 10.1214/aoap/1019487358

Subjects:
Primary: 65U05
Secondary: 60H10

Keywords: Adaption , asymptotic optimality , pathwise approximation , step-size control , Systems of stochastic differential equations

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.10 • No. 2 • May 2000
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