On the convergence of generalized polynomial chaos expansions
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 2, p. 317-339

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.

DOI : https://doi.org/10.1051/m2an/2011045
Classification:  33C45,  35R60,  40A30,  41A10,  60H35,  65N30
Keywords: equations with random data, polynomial chaos, generalized polynomial chaos, Wiener-Hermite expansion, Wiener integral, determinate measure, moment problem, stochastic Galerkin method, spectral elements
@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},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {2},
     year = {2012},
     pages = {317-339},
     doi = {10.1051/m2an/2011045},
     zbl = {1273.65012},
     mrnumber = {2855645},
     language = {en},
     url = {http://www.numdam.org/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, Volume 46 (2012) no. 2, pp. 317-339. doi : 10.1051/m2an/2011045. http://www.numdam.org/item/M2AN_2012__46_2_317_0/

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