ISBN 9783843932820

978-3-8439-3282-0, Reihe Mathematik

Jens Oettershagen
Construction of Optimal Cubature Algorithms with Applications to Econometrics and Uncertainty Quantification

181 Seiten, Dissertation Rheinische Friedrich-Wilhelms-Universität Bonn (2017), Softcover, B5

Zusammenfassung / Abstract

Optimal integration methods for multivariate functions from tensor products of reproducing kernel Hilbert spaces are constructed, analyzed and implemented. Besides optimal weights for random point sets, sparse tensor products of optimal univariate quadrature rules are employed.

As an application of the developed algorithms, this thesis deals with model problems from uncertainty quantification of parametric differential equations. Moreover, discrete choice models from econometrics are considered, since here multivariate integrals often play an important role as well.