Functional limit theorems for certain intrinsic volumes of excursion sets of random fields

Abstract

In the first part of this thesis we develop a method to compute all d+1 intrinsic volumes multigrid convergently for the class of unions of compact sets with positive reach given a digitization. In the second part we prove two functional limit theorems for the volume of excursion sets and for the (d-1)-dimensional Hausdorff measure of level sets of random fields, respectively. As a corollary, we prove large deviation results and propose an asymptotical significance test.