Normal approximation of Kabanov-Skorohod integrals on Poisson spaces

TL;DR

This paper develops bounds for normal approximation of Kabanov-Skorohod integrals on Poisson spaces using the Malliavin-Stein method, with applications to point process statistics and Pareto optimal points.

Contribution

It introduces new bounds involving difference operators for the normal approximation of Kabanov-Skorohod integrals on Poisson spaces, extending existing methods.

Findings

Derived bounds for Wasserstein and Kolmogorov distances

Applied results to linear statistics of point processes

Analyzed functionals related to Pareto optimal points

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.