Asymptotically Optimal Weighted Numerical Integration
Copyright policy )Asymptotically Optimal Weighted Numerical Integration
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].
Preprint: Weierstraß-Institut für Angewandte Analysis und Stochastik, vol. 318
- Weierstrass Institute for Applied Analysis and Stochastics Germany
- Leibniz Association Germany
- Weierstrass Institute Germany
ddc:510, Statistics and Probability, Numerical Analysis, Algebra and Number Theory, Control and Optimization, Hölder-type functions, Applied Mathematics, article, asymptotically optimal design., weighted integration -- probability metric -- asymptotically optimal design, Numerical quadrature and cubature formulas, asymptotically optimal design, Approximate quadratures, weighted integration, 510, probability metric, Brownian paths, numerical integration
ddc:510, Statistics and Probability, Numerical Analysis, Algebra and Number Theory, Control and Optimization, Hölder-type functions, Applied Mathematics, article, asymptotically optimal design., weighted integration -- probability metric -- asymptotically optimal design, Numerical quadrature and cubature formulas, asymptotically optimal design, Approximate quadratures, weighted integration, 510, probability metric, Brownian paths, numerical integration
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