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Normal approximation of Kabanov–Skorohod Integrals on poisson spaces
Citation Link: https://doi.org/10.15480/882.8873
Publikationstyp
Journal Article
Date Issued
2024-06
Sprache
English
TORE-DOI
Volume
37
Issue
2
Start Page
1124
End Page
1167
Citation
Journal of Theoretical Probability 37 (2): 1124-1167 (2024)
Publisher DOI
Scopus ID
We consider the normal approximation of Kabanov–Skorohod integrals on a general Poisson space. Our bounds are for the Wasserstein and the Kolmogorov distance and involve only difference operators of the integrand of the Kabanov–Skorohod integral. The proofs rely on the Malliavin–Stein method and, in particular, on multiple applications of integration by parts formulae. As examples, we study some linear statistics of point processes that can be constructed by Poisson embeddings and functionals related to Pareto optimal points of a Poisson process.
Subjects
Kabanov–Skorohod integral
Malliavin calculus
Normal approximation
Poisson process
Stein’s method
DDC Class
510: Mathematics
Publication version
publishedVersion
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