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January, 1993 Central Limit Properties of GZH-Semigroups and Their Applications in Probability Theory
Yuanjiang He
Ann. Probab. 21(1): 185-201 (January, 1993). DOI: 10.1214/aop/1176989400


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.


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Yuanjiang He. "Central Limit Properties of GZH-Semigroups and Their Applications in Probability Theory." Ann. Probab. 21 (1) 185 - 201, January, 1993.


Published: January, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0771.60020
MathSciNet: MR1207222
Digital Object Identifier: 10.1214/aop/1176989400

Primary: 60F05
Secondary: 22A15 , 43A35 , 60B15

Keywords: Delphic semigroups , GMD-semigroups , GZH-semigroups , infinitesimal array limits , positive definite kernels , probability measures on groups

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 1 • January, 1993
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