Hug, Daniel; Klatt, Michael A.; Last, Günter; Schulte, Matthias (2017). Second order analysis of geometric functionals of Boolean models. In: Vedel Jensen, Eva B.; Kiderlen, Markus (eds.) Tensor valuations and their applications in stochastic geometry and imaging. Lecture Notes in Mathematics: Vol. 2177 (pp. 339-383). Cham: Springer 10.1007/978-3-319-51951-7_12
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This paper 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.
Item Type: |
Book Section (Book Chapter) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |
UniBE Contributor: |
Schulte, Matthias |
Subjects: |
300 Social sciences, sociology & anthropology > 360 Social problems & social services 500 Science > 510 Mathematics 500 Science |
ISSN: |
0075-8434 |
ISBN: |
978-3-319-51950-0 |
Series: |
Lecture Notes in Mathematics |
Publisher: |
Springer |
Language: |
English |
Submitter: |
Matthias Schulte |
Date Deposited: |
20 Mar 2018 10:40 |
Last Modified: |
05 Dec 2022 15:11 |
Publisher DOI: |
10.1007/978-3-319-51951-7_12 |
BORIS DOI: |
10.7892/boris.112844 |
URI: |
https://boris.unibe.ch/id/eprint/112844 |
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