Normal Approximation of Kabanov–Skorohod Integrals on Poisson Spaces

G. Last (), I. Molchanov () and M. Schulte ()
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G. Last: Institute for Stochastics, Karlsruhe Institute of Technology
I. Molchanov: University of Bern
M. Schulte: Hamburg University of Technology

Journal of Theoretical Probability, 2024, vol. 37, issue 2, 1124-1167

Abstract: 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.

Keywords: Kabanov–Skorohod integral; Poisson process; Normal approximation; Stein’s method; Malliavin calculus; Primary: 60F05; Secondary: 60G55; 60H05; 60H07 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01287-0

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