A version of Hormander's theorem for the fractional Brownian motion

• 成果类型: Article
• 署名作者: Baudoin, Fabrice; Hairer, Martin
• 署名单位: University of Warwick; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0035-0
• 发表日期: 2007
• 页码: 373-395
• 关键词: integration; calculus

摘要

It is shown that the law of an SDE driven by fractional Brownian motion with Hurst parameter greater than 1/2 has a smooth density with respect to Lebesgue measure, provided that the driving vector fields satisfy Hormander's condition. The main new ingredient of the proof is an extension of Norris' lemma to this situation.