ON FRACTIONAL SMOOTHNESS AND Lp-APPROXIMATION ON THE GAUSSIAN SPACE

• 成果类型: Article
• 署名作者: Geiss, Stefan; Toivola, Anni
• 署名单位: University of Jyvaskyla; University of Innsbruck
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP884
• 发表日期: 2015
• 页码: 605-638
• 关键词: black-scholes model; STOCHASTIC INTEGRALS; sobolev spaces; Discretization; interpolation; error

摘要

We consider Gaussian Besov spaces obtained by real interpolation and Riemann-Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension. The results are applied to study an approximation problem in L-p for 2 <= p < infinity for stochastic integrals with respect to the d-dimensional (geometric) Brownian motion.