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ANOVA decomposition of convex piecewise linear functions

Please always quote using this URN:urn:nbn:de:0296-matheon-11636
  • Piecewise linear convex functions arise as integrands in stochastic programs. They are Lipschitz continuous on their domain, but do not belong to tensor product Sobolev spaces. Motivated by applying Quasi-Monte Carlo methods we show that all terms of their ANOVA decomposition, except the one of highest order, are smooth if the underlying densities are smooth and certain geometric condition is satisfied. The latter condition is generically satisfied in the normal case.

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Metadaten
Author:Werner Roemisch
URN:urn:nbn:de:0296-matheon-11636
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/08/02
Release Date:2012/08/02
Tag:
Institute:Humboldt-Universität zu Berlin
MSC-Classification:00-XX GENERAL / 00Bxx Conference proceedings and collections of papers / 00B20 Proceedings of conferences of general interest
Preprint Number:979
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