A note on Malliavin fractional smoothness for Lévy processes and approximation

Abstract

Assume a Lévy process $X$ on the time interval $[0,1]$ that is an $L_2$-martingale and let $Y$ be either its stochastic exponential or $X$ itself. We consider Riemann-approximations of certain stochastic integrals driven by $Y$ and relate the $L_2$-approximation rates to the Malliavin fractional smoothness of the integral to be approximated. The Malliavin fractional smoothness is described by Besov spaces generated with the real interpolation method.

Cited by in corpus (2)

• On fractional smoothness and $L_p$-approximation on the Gaussian space
• Permutation Invariant Functionals of Lévy Processes