Journal of Statistical Physics

, Volume 136, Issue 1, pp 89–102 | Cite as

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

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


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.


Isserlis’ theorem Wick’s theorem Mixed-Gaussian distribution Auto-bispectral density 


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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

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