SOME MULTIVARIATE INFINITELY DIVISIBLE DISTRIBUTIONS ANDTHEIR PROJECTIONS

Makoto Maejima Kenjiro Suzuki Yozo Tamura

Abstract: Recently K. Sato constructed an infinitely divisible probability distribution on
such that is not selfdecomposable but every projection of to a lower dimensional
space is selfdecomposable. Let be the Urbanik-Sato type nested
subclasses of the class of all selfdecomposable distributions on In this paper,
for each a probability distribution with the following properties is
constructed: belongs to but every projection of to
a lower -dimensional space belongs to It is also shown that Sato’s
example is not only “non-selfdecomposable” but also “non-semi-selfdecomposable”.