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Quadrature Formulas for the Wiener Measure

✍ Scribed by Achim Steinbauer

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
285 KB
Volume
15
Category
Article
ISSN
0885-064X

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✦ Synopsis

We present a new method for the approximation of Wiener integrals and provide an explicit error bound for a class F of smooth integrands. The purely deterministic algorithm is a sequence of quadrature formulas for the Wiener measure, where the knots are piecewise linear functions. It uses ideas of Smolyak, as well as the multiscale decomposition of the Wiener measure due to Le vy and Ciesielski. For the class F we obtain n(=) max(1, 2= &4 ), where n(=) is the number of integrand evaluations needed to guarantee an error at most = for f # F.

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