In 1972, K. Urbanik introduced the notion of operator-selfdecomposable probability measures (originally they were called Levy's measures). These measures are identified as limit distributions of partial sums of independent Banach space-valued random vectors normed by linear bounded operators. Recently, S. J. Wolfe has characterized the operator-selfdecomposable measures among the infinitely divisible ones. In this note we find examples of measures whose finite convolutions are a dense subset in a class of all operator-selfdecomposable ones.
Publié le : 1982-08-14
Classification:
Banach space,
infinitely divisible measure,
generalized Poisson exponent,
operator-selfdecomposable measures,
one-parameter semi-group of bounded linear operators,
60B10,
60F05
@article{1176993796,
author = {Jurek, Zbigniew J.},
title = {Structure of a Class of Operator-Selfdecomposable Probability Measures},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 849-856},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993796}
}
Jurek, Zbigniew J. Structure of a Class of Operator-Selfdecomposable Probability Measures. Ann. Probab., Tome 10 (1982) no. 4, pp. 849-856. http://gdmltest.u-ga.fr/item/1176993796/