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.
Author: | Werner Roemisch |
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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 |