A generalized Isserlis theorem for location mixtures of Gaussian random vectors |
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Authors: | C Vignat |
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Institution: | E.P.F.L., L.T.H.I., Lausanne, Switzerland |
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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. |
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Keywords: | Isserlis theorem Normal-variance mixture Generalized hyperbolic distribution |
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