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The class of type G distributions on R d and its nested subclasses are studied. An analytic characterization in terms of Levy measures for the class of type G distributions is known. In this paper, probabilistic characterizations by stochastic integral representations for all classes are shown, and analytic characterizations for the nested subclasses are given in terms of Levy measures.

Characterizations of subclasses of type G distributions on $ℝ^d$ by stochastic integral representations