On fractional smoothness and $L_p$-approximation on the Gaussian space

Stefan Geiss; Anni Toivola

doi:10.1214/13-AOP884

On fractional smoothness and $L_p$-approximation on the Gaussian space

Probability 2015-03-09 v2

Authors: Stefan Geiss , 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.

Keywords

fractional smoothness Gaussian Besov spaces real interpolation Riemann-Liouville operators heat extension stochastic integrals Brownian motion

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@article{arxiv.1206.5415,
  title  = {On fractional smoothness and $L_p$-approximation on the Gaussian space},
  author = {Stefan Geiss and Anni Toivola},
  journal= {arXiv preprint arXiv:1206.5415},
  year   = {2015}
}

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Published in at http://dx.doi.org/10.1214/13-AOP884 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

On fractional smoothness and $L_p$-approximation on the Gaussian space

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