Asymptotically optimal weigthed numerical integration
- Mathé, Peter
2010 Mathematics Subject Classification
- 65D32 62E20
- weighted integration, probability metric, asymptotically optimal design
We study numerical integration of Hölder-type functions with respect to weights on the real line. Our study extends previous work by F. Curbera,  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., .
- J. Complexity, 14 (1998), pp. 34-48