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.
|Title of host publication||Tensor Valuations and Their Applications in Stochastic Geometry and Imaging|
|Editors||Eva B. Vedel Jensen, Markus Kiderlen|
|Number of pages||45|
|Publication status||Published - 2017|
|Name||Lecture Notes in Mathematics|