Preprint No.
A-00-08
Thomas Müller-Gronbach
The Optimal Uniform Approximation of Systems of Stochastic Differential Equations
Abstract: 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.
Keywords: systems of stochastic differential equations, pathwise uniform approximation, asymptotic optimality, adaptive method
Mathematics Subject Classification (MSC91):
65U05, 60H10
Language: ENG
Available: Pr-A-00-08.ps
Contact: Thomas Müller-Gronbach, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (gronbach@math.fu-berlin.de)
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