WIAS Preprint No. 318, (1997)

Asymptotically optimal weigthed numerical integration


Authors

  • Mathé, Peter
    ORCID: 0000-0002-1208-1421

2010 Mathematics Subject Classification

  • 65D32 62E20

Keywords

  • weighted integration, probability metric, asymptotically optimal design

DOI

10.20347/WIAS.PREPRINT.318

Abstract

We study numerical integration of Hölder-type functions with respect to weights on the real line. Our study extends previous work by F. Curbera, [2] and relies on a connection between this problem and the approximation of distribution functions by empirical ones. The analysis is based on a lemma which is important within the theory of optimal designs for approximating stochastic processes.

As an application we reproduce a variant of the well known result for weighted integration of Brownian paths, see e.g., [8].

Appeared in

  • J. Complexity, 14 (1998), pp. 34-48

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