A note on Malliavin fractional smoothness for Lévy processes and approximation

Details A note on Malliavin fractional smoothness for Lévy processes and approximation A note on Malliavin fractional smoothness for Lévy processes and approximation

2012-01-01

arxiv.org/abs/1201.0389v1

Mathematics

Probability

Scientific paper

Assume a L\'evy 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.

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