We prove a new class of inequalities, yielding bounds for the normal approximation in the
Wasserstein and the Kolmogorov distance of functionals of a general Poisson process …

Stochastic geometry is the branch of mathematics that studies geometric structures
associated with random configurations, such as random graphs, tilings and mosaics. Due to …

We combine Malliavin calculus with Stein's method to derive bounds for the Variance-
Gamma approximation of functionals of isonormal Gaussian processes, in particular of …

We develop a new quantitative approach to a multidimensional version of the well-known de
Jong's central limit theorem under optimal conditions, stating that a sequence of Hoeffding …

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

For a given homogeneous Poisson point process in R d two points are connected by an
edge if their distance is bounded by a prescribed distance parameter. The behavior of the …

We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener
space, where the target distribution is given by a possibly multidimensional mixture of …

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 …

This chapter provides a detailed and unified discussion of a collection of recently introduced
techniques, allowing one to establish limit theorems with explicit rates of convergence, by …