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Nested subclasses of some subclass of the class of type G selfdecomposable distributions on Rd

Aoyama T.

Probability and Mathematical Statistics

2009

Vol. 29, Fasc. 1

135--154

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.