We establish inequalities for assessing the distance between the distribution of a (possibly
multidimensional) functional of a Poisson random measure and that of a Gaussian element …

We prove a fourth moment bound without remainder for the normal approximation of random
variables belonging to the Wiener chaos of a general Poisson random measure. Such a …

Given a vector F=(F_1,...,F_m) of Poisson functionals F_1,...,F_m, we investigate the
proximity between F and an m-dimensional centered Gaussian random vector N_Σ with …

We consider sequences of symmetric U-statistics, not necessarily Hoeffding-degenerate,
both in a one-and multi-dimensional setting, and prove quantitative central limit theorems …

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 …

Adapting the spectral viewpoint suggested in (Ann. Probab. 40 (6)(2012) 2439–2459) in the
context of symmetric Markov diffusion generators and recently exploited in the non-diffusive …

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 …

We prove tail and moment inequalities for multiple stochastic integrals on the Poisson space
and for Poisson $ U $-statistics. We use them to demonstrate the Law of the Iterated …

In this paper we develop a stochastic analysis for marked binomial processes, that can be
viewed as the discrete analogues of marked Poisson processes. The starting point is the …