An Isserlis' theorem for mixed Gaussian variables: Application to the auto-bispectral density
type: Item
instance of: scholarly article
title: An Isserlis' theorem for mixed Gaussian variables: Application to the auto-bispectral density
zbMATH Open document ID: 1179.60047
author: N. E. Zubov
published in: Journal of Statistical Physics
publication date: 2009-09-09T00:00:00Z
review text: This paper deals with a version of Isserlis theorem for specific case of four mixed-Gaussian random variables. Isserlis theorem can be used to relate the expectation of products of even numbers of normalized, jointly Gaussian random variables to the sum of averages of products of pairs of these variables. The theorem is then used to derive an expression for the auto-bispectral density for quadratically nonlinear systems driven with mixed-Gaussian iid noise.
Mathematics Subject Classification ID: 60H40
Mathematics Subject Classification ID: 81T25
zbMATH DE Number: 5602575
zbMATH Keywords: Isserlis' theorem
zbMATH Keywords: Wick's theorem
zbMATH Keywords: mixed-Gaussian distribution
zbMATH Keywords: auto-bispectral density
reviewed by: N. G. Gamkrelidze
MaRDI profile type: Publication
full work available at URL: s10955-009-9768-3
OpenAlex ID: W1977880122
cites work: An Introduction to Polyspectra
cites work: Asymptotic bias and variance of conventional bispectrum estimates for 2-D signals
cites work: Wick’s theorem for nonsymmetric normal ordered products and contractions
cites work: Higher order cumulants and cumulant spectra
cites work: Q5361362
cites work: Q3967411
cites work: The Evaluation of the Collision Matrix
cites work: Nonlinearity in experimental modal analysis
DOI: 10.1007/S10955-009-9768-3
description: scientific article; zbMATH DE number 5602575