The Levy-Ito decomposition in free probability

• 成果类型: Article
• 署名作者: Barndorff-Nielsen, OE; Thorbjornsen, S
• 署名单位: Aarhus University; University of Southern Denmark
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-003-0322-y
• 发表日期: 2005
• 页码: 197-228
• 关键词: attraction; domains

摘要

In this paper we prove the free analog of the Levy-Ito decomposition for Levy processes. A significant part of the proof consists of introducing free Poisson random measures, proving their existence and developing a theory of integration with respect to such measures. The existence of free Poisson random measures also yields, via the free Levy-Ito decomposition, an alternative proof of the general existence of free Levy processes ( in law).