The Poisson process, a core object in modern probability, enjoys a richer theory than is
sometimes appreciated. This volume develops the theory in the setting of a general abstract …

We consider the topology of simplicial complexes with vertices the points of a random point
process and faces determined by distance relationships between the vertices. In particular …

This chapter develops some basic theory for the stochastic analysis of Poisson process on a
general σ-finite measure space. After giving some fundamental definitions and properties …

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 …

We establish presumably optimal rates of normal convergence with respect to the
Kolmogorov distance for a large class of geometric functionals of marked Poisson and …

The union of the particles of a stationary Poisson process of compact (convex) sets in
Euclidean space is called Boolean model and is a classical topic of stochastic geometry. In …

We establish new explicit bounds on the Gaussian approximation of Poisson functionals
based on novel estimates of moments of Skorohod integrals. Combining these with the …

Supplement to “Limit theory for geometric statistics of point processes having fast decay of
correlations”. This supplement contains various auxiliary facts needed in the proofs. These …

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 …

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 …