Preprint No.
A-98-09
Norbert Hofmann, Thomas Müller-Gronbach, Klaus Ritter
Optimal Approximation of Stochastic Differential Equations by Adaptive Step-Size Control
Abstract: We study the pathwise (strong) approximation of scalar
stochastic differential equations with respect to
the global error in the $L_2$-norm. We introduce an
adaptive step-size control for the Euler scheme.
For equations with additive noise this method is
asymptotically optimal in the class of arbitrary methods
that use a fixed number of observations of the driving
Brownian motion. The superiority of the new method
is confirmed in simulation experiments for equations with
additive noise as well as for general scalar equations.
Keywords: Stochastic differential equations, pathwise approximation, step-size control, asymptotic optimality
Mathematics Subject Classification (MSC91): 65U05 Numerical methods in probability and statistics, 60H10 Stochastic ordinary differential equations [See also 34F05]
Language: ENG
Available: Pr-A-98-09.ps
Contact: Müller-Gronbach, Thomas; Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (gronbach@math.fu-berlin.de)
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