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Contents of PMS, Vol. 29, Fasc. 1,
pages 135 - 154
 

NESTED SUBCLASSES OF SOME SUBCLASS OF THE CLASS OF TYPE G SELFDECOMPOSABLE DISTRIBUTIONS ON RD

TAKAHIRO AOYAMA

Abstract: Nested subclasses, denoted by M (Rd), n = 1,2,... n , 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 M (Rd), n = 1,2,... n , 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.

2000 AMS Mathematics Subject Classification: Primary: 60E07; Secondary: 62E10.

Keywords and phrases: Infinitely divisible distribution on Rd ; type G distribution; selfdecomposable distribution; stochastic integral representation; Lévy process.

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