期刊名称：Brazilian Journal of Probability and Statistics
印刷版ISSN：0103-0752
出版年度：2017
卷号：31
期号：1
页码：144-159
DOI：10.1214/15-BJPS306
语种：English
出版社：Brazilian Statistical Association
摘要：This paper considers multivariate Gaussian fields with their associated matrix valued covariance functions. In particular, we characterize the class of stationary-isotropic matrix valued covariance functions on $d$-dimensional Euclidean spaces, as being the scale mixture of the characteristic function of a $d$ dimensional random vector being uniformly distributed on the spherical shell of $\mathbb{R}^{d}$, with a uniquely determined matrix valued and signed measure. This result is the analogue of celebrated Schoenberg theorem, which characterizes stationary and isotropic covariance functions associated to an univariate Gaussian fields.
