Computing the moments of the Complex Gaussian: Full and sparse covariance matrix

Abstract

Given a multivariate complex centered Gaussian vector Z = (Z 1 , . . ., Z p ) with non-singular covariance matrix S, we derive sufficient conditions on the nullity of the complex moments and we give a closed-form expression for the non-null complex moments. We present conditions for the factorisation of the complex moments. Computational consequences of these results are discussed.