Nested classes of C-decomposable laws

• 成果类型: Article
• 署名作者: Bunge, J
• 署名单位: Cornell University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1997
• 页码: 215-229
• 关键词: PROBABILITY-MEASURES; SPACES

摘要

A random variable X is C-decomposable if X = (D) cX + Y-c for all c in C, where Y-c is a random variable independent of X and C is a closed multiplicative subsemigroup of [0, 1]. X is self-decomposable if C = [0, 1]. Extending an idea of Urbanik in the self-decomposable case, we define a decreasing sequence of subclasses of the class of C-decomposable laws, for any C. We give a structural representation for laws in these classes, and we show that laws in the limiting subclass are infinitely divisible. We also construct noninfinitely divisible examples, some of which are continuous singular.