We characterize the class of linear operators on a finite dimensional inner product space which are the exponents of a full operator-stable law. This answers a question of Paulauskas [6] concerning those operator-stable laws whose characteristic functions are the exponential of quadratic forms. The symmetry group of such laws must be conjugate to the group of all orthogonal transformations on the space.
Publié le : 1982-08-14
Classification:
Operator-stable distributions,
multivariate stable laws,
central limit theorem,
60E05
@article{1176993770,
author = {Holmes, J. P. and Hudson, William N. and Mason, J. David},
title = {Operator-Stable Laws: Multiple Exponents and Elliptical Symmetry},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 602-612},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993770}
}
Holmes, J. P.; Hudson, William N.; Mason, J. David. Operator-Stable Laws: Multiple Exponents and Elliptical Symmetry. Ann. Probab., Tome 10 (1982) no. 4, pp. 602-612. http://gdmltest.u-ga.fr/item/1176993770/