A Poisson or a binomial process on an abstract state space and a symmetric function f acting
on k-tuples of its points are considered. They induce a point process on the target space of f …

This paper deals with Poisson processes on an arbitrary measurable space. Using a direct
approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-Itô …

Stochastic geometry studies randomly generated geometric objects. The present chapter
deals with some discrete aspects of stochastic geometry. We describe work that has been …

This paper deals with the quantitative normal approximation of non-linear functionals of
Poisson random measures, where the quality is measured by the Kolmogorov distance …

Abstract Peccati, Solè, Taqqu, and Utzet recently combined Stein's method and Malliavin
calculus to obtain a bound for the Wasserstein distance of a Poisson functional and a …

This paper deals with U-statistics of Poisson processes and multiple Wiener-Itô integrals on
the Poisson space. Via sharp bounds on the cumulants for both classes of random variables …

AU-statistic of order k with kernel f: X^ k → R^ d over a Poisson process η is defined as ∑ _
(x_ 1, ..., x_ k) f (x_ 1, ..., x_ k), where the summation is over k-tuples of distinct points of η …

Let η t be a Poisson point process with intensity measure tμ, t> 0, over a Borel space X,
where μ is a fixed measure. Another point process ξ t on the real line is constructed by …

This chapter introduces some of the fundamental notions from stochastic geometry.
Background information from convex geometry is provided as far as this is required for the …

In this thesis, abstract bounds for the normal approximation of Poisson functionals are
computed by the Malliavin-Stein method and used to derive central limit theorems for …