Second order analysis of geometric functionals of Boolean models

Daniel Hug, Michael A. Klatt, Günter Last, Matthias Schulte

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

Abstract

This chapter presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.
Original languageEnglish
Title of host publicationTensor Valuations and Their Applications in Stochastic Geometry and Imaging
EditorsEva B. Vedel Jensen, Markus Kiderlen
PublisherSpringer
Pages339-383
Number of pages45
ISBN (Electronic)9783319519517
ISBN (Print)9783319519500
DOIs
Publication statusPublished - 2017

Publication series

NameLecture Notes in Mathematics
Volume2177
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

Fingerprint Dive into the research topics of 'Second order analysis of geometric functionals of Boolean models'. Together they form a unique fingerprint.

Cite this