REPRESENTATIONS AND ISOMORPHISM IDENTITIES FOR INFINITELY DIVISIBLE PROCESSES

• 成果类型: Article
• 署名作者: Rosinski, Jan
• 署名单位: University of Tennessee System; University of Tennessee Knoxville
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1246
• 发表日期: 2018
• 页码: 3229-3274
• 关键词: series

摘要

We propose isomorphism-type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron-Martin formula for Poissonian infinitely divisible processes but with random translations. The applicability of such tools relies on precise understanding of Levy measures of infinitely divisible processes and their representations, which are studied here in full generality. We illustrate this approach on examples of squared Bessel processes, Feller diffusions, permanental processes, as well as Levy processes.