Vignat, C and Bhatnagar, S (2008) An extension of Wick's theorem. In: Statistics & Probability Letters, 78 (15). pp. 2404-2407.
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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.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Elsevier Science.|
|Department/Centre:||Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)|
|Date Deposited:||04 Sep 2009 10:28|
|Last Modified:||19 Sep 2010 04:57|
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