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”.
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”.