% You need the following packages in the main file to let this entry work: % \usepackage[english,ngerman]{babel} multilingual support % \usepackage{url} urls formatting % \usepackage{hyperref} make url klickable, recommended % Just put them into the preamble of the main .tex-file. % You should possibly make some changes to the typography of this entry, % e.g. quotation marks. % Which fields of this entry will be shown in the bibliography depends on the bibtex-style, which you use @incollection{oai:export, author = {Holger Heitsch and Hernan Leövey and Werner Römisch}, title = {Are Quasi-Monte Carlo algorithms efficient for two-stage stochastic programs?}, series = {Stochastic Programming E-Print Series}, year = {2012}, publisher = {Institut für Mathematik}, editor = { Julie L.  Higle and Werner  Römisch and Surrajeet  Sen }, WernerRömischSurrajeetSenabstract = {Quasi-Monte Carlo algorithms are studied for designing discrete approximations of two-stage linear stochastic programs. Their integrands are piecewise linear, but neither smooth nor lie in the function spaces considered for QMC error analysis. We show that under some weak geometric condition on the two-stage model all terms of their ANOVA decomposition, except the one of highest order, are smooth. Hence, Quasi-Monte Carlo algorithms may achieve the optimal rate of convergence $O(n^{-1+\delta}$ with $\delta \in (0,\frac{1}{2}]$ and a constant not depending on the dimension. The geometric condition is shown to be generically satis fied if the underlying distribution is normal. We discuss sensitivity indices, e ffective dimensions and dimension reduction techniques for two-stage integrands. Numerical experiments show that indeed convergence rates close to the optimal rate are achieved when using randomly scrambled Sobol' point sets and randomly shifted lattice rules accompanied with suitable dimension reduction techniques.}, note = {unpublished} url = { \url{http://edoc.hu-berlin.de/docviews/abstract.php?id=39574} }, url = { \url{urn:nbn:de:kobv:11-100204148} }, number = { 5}, timestamp = {2015-10-06T12:29:04Z} }