Non-Gaussian simulation using Hermite polynomial expansion: convergences and algorithms

By B. Puig, F. Poirion, Christian Soize. 2002

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Simulation of simply cross correlated random fields by series expansion methods (2008, unknown): “[42] utilized Hermite polynomial chaos method.”
The stochastic finite element method: Past, present and future (2009, methodology): “[149,150] examined the convergence behaviour of PC expansion and proposed an optimization technique for the determination of the underlying Gaussian autocorrelation function.”
Simulation of strongly non-Gaussian processes using Karhunen–Loeve expansion (2005, methodology): “Recent attempts utilize the Hermite polynomial chaos method ([14] [15] [16]).”
Fast Numerical Methods for Stochastic Computations: A Review (2009, background): “This remains an active research, see, for example, [32, 60, 61, 63, 70, 102].”
A multi‐scale spectral stochastic method for homogenization of multi‐phase periodic composites with random material properties (2010, methodology): “In this section, we show how this information can be used to construct a series expansion in terms of one-dimensional Hermite polynomials that has approximately the same distribution as the distribution of the input random variable [20].”
Simulation of non-Gaussian processes using fractile correlation (2004, background): “[12] believed that this is not always possible, partially because the underlying Gaussian correlation function has to be non-negative definite.”