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arXiv · 1605.07413

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

Eija Laukkarinen
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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.

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Eija Laukkarinen. 2016-05-24. A note on Malliavin smoothness on the L\'evy space. https://arxiv.org/abs/1605.07413

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