A new factorization property of the selfdecomposable probability measures

• 成果类型: Article
• 署名作者: Iksanov, AM; Jurek, ZJ; Schreiber, BM
• 署名单位: Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; University of Wroclaw
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000225
• 发表日期: 2004
• 页码: 1356-1369
• 关键词: banach-spaces; distributions; REPRESENTATION; levy

摘要

We prove that the convolution of a selfdecomposable distribution with its background driving law is again selfdecomposable if and only if the background driving law is s-selfdecomposable. We will refer to this as the factorization property of a selfdecomposable distribution; let L-f denote the set of all these distributions. The algebraic structure and various characterizations of L-f are studied. Some examples are discussed, the most interesting one being given by the Levy stochastic area integral. A nested family of subclasses L-n(f), n greater than or equal to 0, (or a filtration) of the class L-f is given.