Nested subclasses, denoted by Mn(Rd); n = 1; 2,…,of the class M(Rd), a subclass of the class of type G and selfdecomposable distributions on Rd are studied. An analytic characterization in terms of Lévy measures and a probabilistic characterization by stochastic integral representations for M(Rd) are known. In this paper, analytic characterizations for Mn(Rd); n = 1; 2,…,are given in terms of Lévy measures as well as probabilistic characterizations by stochastic integral representations are shown. A relationship with stable distributions is given.
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Classes of infinitely divisible distributions obtained by iteration of Gaus-sian randomization of Levy measures are introduced and studied. Their relation to Urbanik-Sato nested classes of selfdecomposable distributions is also established.
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