Free-knot spline approximation of stochastic processes

Authors:
Jakob Creutzig;Thomas Müller-Gronbach;Klaus Ritter
Affiliations:
Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstraße 7, 64289 Darmstadt, Germany;Fakultät für Mathematik und Informatik, FernUniversität Hagen, Lützowstraße 125, 58084 Hagen, Germany;Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstraße 7, 64289 Darmstadt, Germany
Venue:
Journal of Complexity
Year:
2007

Citing 5
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Abstract

We study optimal approximation of stochastic processes by polynomial splines with free knots. The number of free knots is either a priori fixed or may depend on the particular trajectory. For the s-fold integrated Wiener process as well as for scalar diffusion processes we determine the asymptotic behavior of the average L"p-distance to the splines spaces, as the (expected) number of free knots tends to infinity.