Linear vs standard information for scalar stochastic differential equations

Authors:
Norbert Hofmann;Thomas Müller-Gronbach;Klaus Ritter
Affiliations:
Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, Postfach 11 19 32, 60054 Frankfurt am Main, Germany;Fachbereich Mathematik, Technische Universitüt Darmstadt, Sehlossgartenstr. 7, 64289 Darmstadt, Germany;Fachbereich Mathematik, Technische Universitüt Darmstadt, Sehlossgartenstr. 7, 64289 Darmstadt, Germany
Venue:
Journal of Complexity
Year:
2002

Citing 4
Cited 2

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On the average complexity of multivariate problems

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The optimal discretization of stochastic differential equations

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On the global error of Itô-Taylor schemes for strong approximation of scalar stochastic differential equations

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Optimal approximation of SDE's with additive fractional noise

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Abstract

We study pathwise approximation of scalar sde's with respect to the mean squared L2-error. We compare the power of linear and standard information about the driving Brownian motion. It turns out that asymptotically the corresponding minimal errors differ only by the factor √6/π.