Mean Euler characteristic of stationary random closed sets

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:137

Article

Rataj, Jan¹ 

[1] Charles Univ Prague, Fac Math & Phys, Sokolovska 83, Prague 18675 8, Czech Republic

关键词: Set with positive reach;    Curvature measure;    Flag measure;    Euler characteristic;    Random closed set;    Gaussian random field;   

DOI  :  10.1016/j.spa.2021.03.012

来源: Elsevier

【 摘 要 】

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 C-1,C-1 realizations, in particular, stationary Gaussian fields, and obtain results which extend those known from the literature. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free