A generalized Isserlis theorem for location mixtures of Gaussian random vectors

C. Vignat

Statistics & Probability Letters, 2012, vol. 82, issue 1, 67-71

Abstract: In a recent paper (Michalowicz et al., 2011), Michalowicz et al. provide an extension of the Isserlis theorem to the case of a Rademacher location mixture of a Gaussian vector. This theorem is known to physicists under the name of Wick’s theorem. We generalize here this result to the case of any location mixture of Gaussian vector; we also provide an example of the extension of the Isserlis theorem to a “scale–location” mixture of Gaussian, namely, the d-dimensional generalized hyperbolic distribution.

Keywords: Isserlis theorem; Normal-variance mixture; Generalized hyperbolic distribution (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2011.09.008

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