We consider two integral transforms which are frequently used in integral geometry and related fields, namely the spherical Radon and cosine transform. Fast algorithms are developed which invert the… Expand

The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on $\mathbb{R}^d$ are proved. Special attention is paid to Gaussian and… Expand

For a Borel set A and a homogeneous Poisson point process η in of intensity λ>0, define the Poisson–Voronoi approximation A η of A as a union of all Voronoi cells with nuclei from η lying in A. If A… Expand

A kriging based on residuals is employed for spatial extrapolation of anisotropic directional road–traffic data to interpret the recorded velocities as realizations of a random velocity field, which is sampled at selected points only.Expand

For parallel neighborhoods of the paths of the d ‐dimensional Brownian motion, so‐called Wiener sausages, formulae for the expected surface area are given for any dimension d ≥ 2. It is shown by… Expand

We study a change-point problem for random fields based on a univariate detection of outliers via the 3σ-rule in order to recognize inhomogeneities in glass fiber reinforced polymers (GFRP). In… Expand

This chapter is a primer on the limit theorems for dependent random fields. First, dependence concepts such as mixing, association and their generalizations are introduced. Then, moment inequalities… Expand