Hypoellipticity in infinite dimensions and an application in interest rate theory

• 成果类型: Article
• 署名作者: Baudoin, F; Teichmann, J
• 署名单位: Technische Universitat Wien
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000214
• 发表日期: 2005
• 页码: 1765-1777
• 关键词: malliavin calculus; EQUATIONS; EXISTENCE

摘要

We apply methods from Malliavin calculus to prove an infinite-dimensional version of Hormander's theorem for stochastic evolution equations in the spirit of Da Prato-Zabczyk. This result is used to show that HJM-equations from interest rate theory, which satisfy the Hormander condition, have the conceptually undesirable feature that any selection of yields admits a density as multi-dimensional random variable.