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

Stefan Geiss; Anni Toivola

doi:10.1214/13-aop884

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arXiv · 1206.5415

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

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.

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Stefan Geiss, Anni Toivola. 2015-03-06. On fractional smoothness and $L_p$-approximation on the Gaussian space. https://doi.org/10.1214/13-aop884

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