ON THE CONVERGENCE OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS
ON THE CONVERGENCE OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS
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DOI：
10.1051/m2an/2011045
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发表时间：
2012-03-01
影响因子：
1.9
通讯作者：
Ullmann, Elisabeth
中科院分区：
文献类型：
--
作者：
Ernst, Oliver G.;Mugler, Antje;Ullmann, Elisabeth
基于随机变量的广义多项式混沌展开式，提出了一种离散随机数据偏微分方程的方法。这些构成推广的多项式混沌展开介绍诺伯特维纳展开多项式正交关于非高斯概率措施。我们提出的条件，这些措施，这意味着广义多项式混沌展开的均方收敛到正确的限制，并补充这些说明性的例子。
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.