Quadrature Formulas for the Wiener Measure

Achim Steinbauer
1999 Journal of Complexity  
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
more » ... ed to guarantee an error at most = for f # F. Academic Press Article ID jcom.1999.0518, available online at http:ÂÂwww.idealibrary.com on 476 0885-064XÂ99 30.00
doi:10.1006/jcom.1999.0518 fatcat:kewuq5p5jfcpfmgnieirnlsvr4