6533b855fe1ef96bd12b1245
RESEARCH PRODUCT
A note on Malliavin smoothness on the Lévy space
Eija Laukkarinensubject
Statistics and ProbabilitySmoothness (probability theory)matematiikkaLévy processMalliavin calculus010102 general mathematicsMalliavin calculus01 natural sciencesLévy processinterpolation010104 statistics & probability60H07Mathematics::ProbabilitySquare-integrable functionCompound Poisson processApplied mathematicsinterpolointiDifferentiable functiontila0101 mathematicsStatistics Probability and UncertaintyLp spaceRandom variable60G51Mathematicsdescription
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. peerReviewed
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-01-01 | Electronic Communications in Probability |