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May 2002 The optimal uniform approximation of systems of stochastic differential equations
Thomas Müller-Gronbach
Ann. Appl. Probab. 12(2): 664-690 (May 2002). DOI: 10.1214/aoap/1026915620


We analyze numerical methods for the pathwise approximation of a system of stochastic differential equations. As a measure of performance we consider the $q$th mean of the maximum distance between the solution and its approximation on the whole unit interval. We introduce an adaptive discretization that takes into account the local smoothness of every trajectory of the solution. The resulting adaptive Euler approximation performs asymptotically optimal in the class of all numerical methods that are based on a finite number of observations of the driving Brownian motion.


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Thomas Müller-Gronbach. "The optimal uniform approximation of systems of stochastic differential equations." Ann. Appl. Probab. 12 (2) 664 - 690, May 2002.


Published: May 2002
First available in Project Euclid: 17 July 2002

zbMATH: 1019.65009
MathSciNet: MR1910644
Digital Object Identifier: 10.1214/aoap/1026915620

Primary: 65U05
Secondary: 60H10

Keywords: adaptive method , asymptotic optimality , pathwise uniform approximation , Systems of stochastic differential equations

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.12 • No. 2 • May 2002
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