The Annals of Applied Probability

The optimal uniform approximation of systems of stochastic differential equations

Thomas Müller-Gronbach

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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.

Article information

Ann. Appl. Probab., Volume 12, Number 2 (2002), 664-690.

First available in Project Euclid: 17 July 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65U05
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05]

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


Müller-Gronbach, Thomas. The optimal uniform approximation of systems of stochastic differential equations. Ann. Appl. Probab. 12 (2002), no. 2, 664--690. doi:10.1214/aoap/1026915620.

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