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An extension of Wick's theorem

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  • Vignat, C.
  • Bhatnagar, S.

Abstract

We propose an extension of a result by Repetowicz et al. [Repetowicz, P., Richmond, P., 2004. The Wick theorem for non-Gaussian distributions and its application for noise filtering of correlated q-exponentially distributed random variables (in press). arxiv:math-ph/0411020 v1] about Wick's theorem and its applications. We first show that Wick's theorem can be extended to the uniform distribution on the sphere and then to the whole class of elliptical distributions. Then, as a special case, we detail this result for distributions that are scale mixtures of Gaussians. Finally, we show that these results allow to recover easily a theorem by Folland [Folland, G.B., 2001. How to integrate a polynomial over a sphere. The American Mathematical Monthly 108 (5), 446-448] about the integration of polynomials over the sphere.

Suggested Citation

  • Vignat, C. & Bhatnagar, S., 2008. "An extension of Wick's theorem," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2404-2407, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2404-2407
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    Cited by:

    1. Vignat, C., 2012. "A generalized Isserlis theorem for location mixtures of Gaussian random vectors," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 67-71.
    2. Michalowicz, J.V. & Nichols, J.M. & Bucholtz, F. & Olson, C.C., 2011. "A general Isserlis theorem for mixed-Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1233-1240, August.

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