Wiener-Hermite Polynomial Expansion for Multivariate Gaussian Probability Measures

Understand

This paper introduces a new generalized polynomial chaos expansion (PCE) comprising multivariate Hermite orthogonal polynomials in dependent Gaussian random variables.

• The second-moment properties of Hermite polynomials reveal a weakly orthogonal system when obtained for a general Gaussian probability measure.
• Still, the exponential integrability of norm allows the Hermite polynomials to constitute a complete set and hence a basis in a Hilbert space.
• The completeness is vitally important for the convergence of the generalized PCE to the correct limit.