CENTRAL LIMIT PROPERTIES OF GZH-SEMIGROUPS AND THEIR APPLICATIONS IN PROBABILITY-THEORY

• 成果类型: Article
• 署名作者: HE, YJ
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989400
• 发表日期: 1993
• 页码: 185-201
• 关键词: decomposition

摘要

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.