We propose an extension of a result by Repetowicz et al. 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 Gaussian scale mixtures. Finally, we show that these results allow to
recover easily a theorem by Folland about integration of polynomials over the
sphere.
%0 Generic
%1 vignat2007extension
%A Vignat, C.
%A Bhatnagar, S.
%D 2007
%K Isserlis distributions moments multivariate probability
%T An extension of Wick's theorem
%U http://arxiv.org/abs/0709.1999
%X We propose an extension of a result by Repetowicz et al. 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 Gaussian scale mixtures. Finally, we show that these results allow to
recover easily a theorem by Folland about integration of polynomials over the
sphere.
@misc{vignat2007extension,
abstract = {We propose an extension of a result by Repetowicz et al. 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 Gaussian scale mixtures. Finally, we show that these results allow to
recover easily a theorem by Folland about integration of polynomials over the
sphere.},
added-at = {2018-01-26T06:46:54.000+0100},
author = {Vignat, C. and Bhatnagar, S.},
biburl = {https://www.bibsonomy.org/bibtex/24ba5221d73b9edae5f0f08585aecbaea/shabbychef},
description = {An extension of Wick's theorem},
interhash = {532ee61a5f891e88791aa400641a5df7},
intrahash = {4ba5221d73b9edae5f0f08585aecbaea},
keywords = {Isserlis distributions moments multivariate probability},
note = {cite arxiv:0709.1999},
timestamp = {2018-01-26T06:48:04.000+0100},
title = {An extension of Wick's theorem},
url = {http://arxiv.org/abs/0709.1999},
year = 2007
}