Type G Distributions on $${\mathbb{R}}$$ d

Makoto Maejima () and Jan Rosiński ()
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Makoto Maejima: Keio University
Jan Rosiński: University of Tennessee

Journal of Theoretical Probability, 2002, vol. 15, issue 2, 323-341

Abstract: 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.

Keywords: variance mixture of normal distribution; type G distributions; Lévy measures; series representations (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1015044726122

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