A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement these with illustrative examples.
@article{M2AN_2012__46_2_317_0,
author = {Ernst, Oliver G. and Mugler, Antje and Starkloff, Hans-J\"org and Ullmann, Elisabeth},
title = {On the convergence of generalized polynomial chaos expansions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {46},
year = {2012},
pages = {317-339},
doi = {10.1051/m2an/2011045},
mrnumber = {2855645},
zbl = {1273.65012},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2012__46_2_317_0}
}
Ernst, Oliver G.; Mugler, Antje; Starkloff, Hans-Jörg; Ullmann, Elisabeth. On the convergence of generalized polynomial chaos expansions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012) pp. 317-339. doi : 10.1051/m2an/2011045. http://gdmltest.u-ga.fr/item/M2AN_2012__46_2_317_0/
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