An Isserlis' Theorem for Mixed Gaussian Variables: Application to the Auto-Bispectral Density
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.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- July 2009
- DOI:
- 10.1007/s10955-009-9768-3
- Bibcode:
- 2009JSP...136...89M
- Keywords:
-
- Isserlis’
- theorem;
- Wick’
- s theorem;
- Mixed-Gaussian distribution;
- Auto-bispectral density;
- Isserlis' theorem;
- Wick's theorem