Journal of Statistical Physics

, Volume 136, Issue 1, pp 89–102

An Isserlis’ Theorem for Mixed Gaussian Variables: Application to the Auto-Bispectral Density

  • J. V. Michalowicz
  • J. M. Nichols
  • F. Bucholtz
  • C. C. Olson
Article

DOI: 10.1007/s10955-009-9768-3

Cite this article as:
Michalowicz, J.V., Nichols, J.M., Bucholtz, F. et al. J Stat Phys (2009) 136: 89. doi:10.1007/s10955-009-9768-3

Abstract

This work derives a version of Isserlis’ theorem for the specific case of four mixed-Gaussian random 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.

Keywords

Isserlis’ theoremWick’s theoremMixed-Gaussian distributionAuto-bispectral density

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • J. V. Michalowicz
    • 1
    • 2
  • J. M. Nichols
    • 1
  • F. Bucholtz
    • 1
  • C. C. Olson
    • 1
  1. 1.Optical Science DivisionU.S. Naval Research LaboratoryWashingtonUSA
  2. 2.SFA, Inc.CroftonUSA