The Annals of Probability

On fractional smoothness and Lp-approximation on the Gaussian space

Stefan Geiss and Anni Toivola

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Abstract

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 $2\le p<\infty$ for stochastic integrals with respect to the $d$-dimensional (geometric) Brownian motion.

Article information

Source
Ann. Probab., Volume 43, Number 2 (2015), 605-638.

Dates
First available in Project Euclid: 2 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aop/1422885571

Digital Object Identifier
doi:10.1214/13-AOP884

Mathematical Reviews number (MathSciNet)
MR3306001

Zentralblatt MATH identifier
1343.60068

Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus 60H05: Stochastic integrals 41A25: Rate of convergence, degree of approximation
Secondary: 46B70: Interpolation between normed linear spaces [See also 46M35] 26A33: Fractional derivatives and integrals

Keywords
Stochastic analysis on a Gaussian space Besov spaces Riemann–Liouville operators real interpolation approximation of stochastic integrals

Citation

Geiss, Stefan; Toivola, Anni. On fractional smoothness and L p -approximation on the Gaussian space. Ann. Probab. 43 (2015), no. 2, 605--638. doi:10.1214/13-AOP884. https://projecteuclid.org/euclid.aop/1422885571


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