A class of topological semigroups called GZH-semigroups is introduced. Conditions under which they have the property that limits of infinitesimal arrays are infinitely divisible are obtained. The convolution semigroup of all probability measures on a second countable LCA-group or on a real separable Hilbert space as well as the semigroup of all positive definite kernels defined on a countable set with complex values and with norms not greater than 1 are reduced to an extended form of Delphic semigroups.
Publié le : 1993-01-14
Classification:
GZH-semigroups,
GMD-semigroups,
Delphic semigroups,
infinitesimal array limits,
probability measures on groups,
positive definite kernels,
60F05,
22A15,
60B15,
43A35
@article{1176989400,
author = {He, Yuanjiang},
title = {Central Limit Properties of GZH-Semigroups and Their Applications in Probability Theory},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 185-201},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989400}
}
He, Yuanjiang. Central Limit Properties of GZH-Semigroups and Their Applications in Probability Theory. Ann. Probab., Tome 21 (1993) no. 4, pp. 185-201. http://gdmltest.u-ga.fr/item/1176989400/