Composition semigroups and random stability

• 成果类型: Article
• 署名作者: Bunge, J
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1065725189
• 发表日期: 1996
• 页码: 1476-1489
• 关键词: DISTRIBUTIONS

摘要

A random variable X is N-divisible if it can be decomposed into a random sum of N i.i.d. components, where N is a random variable independent of the components; X is N-stable if the components are rescaled copies of X. These N-divisible and N-stable random variables arise in a variety of stochastic models, including thinned renewal processes and subordinated Levy and stable processes. We consider a general theory of N-divisibility and N-stability in the case where E(N) < infinity, based on a representation of the probability generating function of N in terms of its limiting Laplace-Stieltjes transform l. We analyze certain topological semigroups of such p.g.f's in detail, and on this basis we extend existing characterizations of N-divisible and N-stable laws in terms of l. We apply the results to the aforementioned stochastic models.