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2000

Optimal approximation of stochastic differential equations by adaptive step-size control

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Optimal approximation of stochastic differential equations by adaptive step-size control
We study the pathwise (strong) approximation of scalar stochastic differential equations with respect to the global error in the L2-norm. For equations with additive noise we establish a sharp lower error bound in the class of arbitrary methods that use a fixed number of observations of the driving Brownian motion. As a consequence, higher order methods do not exist if the global error is analyzed. We introduce an adaptive step-size control for the Euler scheme which performs asymptotically optimally. In particular, the new method is more efficient than an equidistant discretization. This superiority is confirmed in simulation experiments for equations with additive noise, as well as for general scalar equations.
Norbert Hofmann, Thomas Müller-Gronbach, Klau
Added 19 Dec 2010
Updated 19 Dec 2010
Type Journal
Year 2000
Where MOC
Authors Norbert Hofmann, Thomas Müller-Gronbach, Klaus Ritter
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