Second order analysis of geometric functionals of Boolean models

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:

25 Oct 2019 22:07

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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