Abstract
This paper presents a systematic study of the class of multivariate distributions obtained by a Gaussian randomization of jumps of a Lévy 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 Lévy 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.
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Maejima, M., Rosiński, J. Type G Distributions on \({\mathbb{R}}\) d . Journal of Theoretical Probability 15, 323–341 (2002). https://doi.org/10.1023/A:1015044726122
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DOI: https://doi.org/10.1023/A:1015044726122