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Mean Euler characteristic of stationary random closed sets

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  • Rataj, Jan

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.

Suggested Citation

  • Rataj, Jan, 2021. "Mean Euler characteristic of stationary random closed sets," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 252-271.
    • Handle: RePEc:eee:spapps:v:137:y:2021:i:c:p:252-271
    DOI: 10.1016/j.spa.2021.03.012
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    References listed on IDEAS

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    1. Cambanis, Stamatis, 1973. "On some continuity and differentiability properties of paths of Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 420-434, December.
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