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

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.

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)

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• On discrete time hedging in d-dimensional option pricing models
• Generalized fractional smoothness and $L_p$-variation of BSDEs with non-Lipschitz terminal condition
• A note on Malliavin fractional smoothness for Lévy processes and approximation
• Fractional smoothness of functionals of diffusion processes under a change of measure

Cited by in corpus (2)

• On the sharpness of embeddings of Hölder spaces into Gaussian Besov spaces
• Convergence rate for the hedging error of a path-dependent example