Normal approximation of Kabanov-Skorohod integrals on Poisson spaces

2022/11/03 by Günter Last, Ilya Molchanov, Last, Günter +3
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Kabanov–Skorohod integral #Malliavin calculus #Mathematical Analysis and Transform Methods #Mathematics #Normal approximation #Poisson process #Stein’s method #advanced mathematical theories

paper · pdf · doi:10.15480/882.8873

openalex publication_date 2022/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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