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March 2015 On fractional smoothness and Lp-approximation on the Gaussian space
Stefan Geiss, Anni Toivola
Ann. Probab. 43(2): 605-638 (March 2015). DOI: 10.1214/13-AOP884

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.

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Stefan Geiss. Anni Toivola. "On fractional smoothness and Lp-approximation on the Gaussian space." Ann. Probab. 43 (2) 605 - 638, March 2015. https://doi.org/10.1214/13-AOP884

Information

Published: March 2015
First available in Project Euclid: 2 February 2015

zbMATH: 1343.60068
MathSciNet: MR3306001
Digital Object Identifier: 10.1214/13-AOP884

Subjects:
Primary: 41A25, 60H05, 60H07
Secondary: 26A33, 46B70

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 2 • March 2015
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