Type G Distributions on Rd

This paper presents a systematic study of the class of multivariate distributions obtained by a Gaussian randomization of jumps of a Levy process. This class, called the class of type G distributions, constitutes a closed convolution semigroup of the family of symmetric infinitely divisible probability measures. Spectral form of Levy measures of type G distributions is obtained and it is shown that type G property can not be determined by one dimensional projections. Conditionally Gaussian structure of type G random vectors is exhibited via series representations.