A note on Malliavin smoothness on the Lévy space
Laukkarinen, E. (2017). A note on Malliavin smoothness on the Lévy space. Electronic Communications in Probability, 22, 34. doi:10.1214/17-ECP65
Published inElectronic Communications in Probability
© the Author, 2017. This is an open access article distributed under the terms of a Creative Commons License.
We consider Malliavin calculus based on the Itô chaos decomposition of square integrable random variables on the Lévy space. We show that when a random variable satisfies a certain measurability condition, its differentiability and fractional differentiability can be determined by weighted Lebesgue spaces. The measurability condition is satisfied for all random variables if the underlying Lévy process is a compound Poisson process on a finite time interval.