Felix Ballani

Random marked sets

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

Reconstruction of random heterogeneous media

Stochastic reconstruction is a technique to generate samples of random structures with prescribed distributional properties in the sense that certain of their statistical summary characteristics match target values or forms. This technique can be used to produce structures of any wanted size for further statistical analysis starting from small samples, which may be even only lower dimensional, for instance, when three‐dimensional imaging techniques are not available. In this review we explain the main ideas of stochastic reconstruction, concentrating on the most important case of digitized binary media and with a particular emphasis on stereological reconstruction.

On Modelling of Refractory Castables by Marked Gibbs and Gibbsian-like Processes

The modelling of self-flowing refractory castables, a special kind of concrete, is discussed. It consists of two phases: a system of randomly distributed spherical hard grains and a cement matrix. The focus is on marked Gibbs and Gibbsian-like processes but also some other models are discussed. It turns out that a particular canonical marked Gibbsian-like process is useful for modelling the samples and more plausible than the classical stationary marked Gibbs process.