On fractional smoothness and Lp-approximation on the Gaussian space

Authors
Geiss, Stefan Toivola, Anni
Citation
Geiss, Stefan et Toivola, Anni, On fractional smoothness and Lp-approximation on the Gaussian space, Annals of probability , 43(2), 2015, pp. 605-638
Journal title
Annals of probability → ACNP
ISSN journal
00911798
Volume
43
Issue
2
Year of publication
2015
Pages
605 - 638
Database
ACNP
SICI code
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 Lp for 2.p<. for stochastic integrals with respect to the d-dimensional (geometric) Brownian motion.