A comprehensive study on seismic dynamic responses of stochastic structures using sparse grid-based polynomial chaos expansion

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

Dongbin Xiu, George Em Karniadakis · SIAM Journal on Scientific Computing · 2002 · 4.7K citations

Natural Sciences, Computational Engineering, Mathematics +16

The Homogeneous Chaos

Norbert Wiener · American Journal of Mathematics · 1938 · 3K citations

Aleatory or epistemic? Does it matter?

Armen Der Kiureghian, Ove Ditlevsen · Structural Safety · 2008 · 2.4K citations

Humanities, Philosophy, Epistemology +3

The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals

R. H. Cameron, W. T. Martin · Annals of Mathematics · 1947 · 1.3K citations

Natural Sciences, Physics, Stochastic Processes +11

A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data

Fabio Nobile, Raúl Tempone, Clayton Webster · SIAM Journal on Numerical Analysis · 2008 · 950 citations · Full text

Computing, Computational Engineering, Finite Element Analysis +13