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Contents of PMS, Vol. 19, Fasc. 2,
pages 421 - 428
 

SOME MULTIVARIATE INFINITELY DIVISIBLE DISTRIBUTIONS AND THEIR PROJECTIONS

Makoto Maejima
Kenjiro Suzuki
Yozo Tamura

Abstract: Recently K. Sato constructed an infinitely divisible probability distribution m on Rd such that m is not selfdecomposable but every projection of m to a lower dimensional space is selfdecomposable. Let L  (Rd),
  m 1 < m <  oo , be the Urbanik-Sato type nested subclasses of the class L (Rd)
 0 of all selfdecomposable distributions on Rd. In this paper, for each 1 < m <  oo , a probability distribution m with the following properties is constructed: m belongs to L    (Rd)  /~\  (L (Rd))c,
 m -1        m but every projection of m to a lower k -dimensional space belongs to L  (Rk).
 m It is also shown that Sato’s example is not only “non-selfdecomposable” but also “non-semi-selfdecomposable”.

1991 AMS Mathematics Subject Classification: Primary -; Secondary -;

Key words and phrases: -

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