English

A note on Malliavin smoothness on the L\'evy space

Probability 2016-05-25 v1

Abstract

We consider Malliavin calculus based on the It\^o chaos decomposition of square integrable random variables on the L\'evy 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 L\'evy process is a compound Poisson process on a finite time interval.

Keywords

Cite

@article{arxiv.1605.07413,
  title  = {A note on Malliavin smoothness on the L\'evy space},
  author = {Eija Laukkarinen},
  journal= {arXiv preprint arXiv:1605.07413},
  year   = {2016}
}
R2 v1 2026-06-22T14:08:11.247Z