Mean Euler characteristic of stationary random closed sets

Jan Rataj

Stochastic Processes and their Applications, 2021, vol. 137, issue C, 252-271

Abstract: The translative intersection formula of integral geometry yields an expression for the mean Euler characteristic of a stationary random closed set intersected with a fixed observation window. We formulate this result in the setting of sets with positive reach and using flag measures which yield curvature measures as marginals. As an application, we consider excursion sets of stationary random fields with C1,1 realizations, in particular, stationary Gaussian fields, and obtain results which extend those known from the literature.

Keywords: Set with positive reach; Curvature measure; Flag measure; Euler characteristic; Random closed set; Gaussian random field (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.03.012

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