平稳随机闭集的平均欧拉示性数
Mean Euler characteristic of stationary random closed sets
摘要：
利用积分几何中的平移交公式，给出了具有固定观测窗的平稳随机闭集序列的平均欧拉示性数的表达式。我们制定了这一结果的设置具有积极的影响，并使用旗措施，产生曲率措施作为边缘。作为一个应用，我们考虑平稳随机场的漂移集与$C^{1,1}$实现，特别是平稳高斯场，并获得结果，这些文献中已知的扩展。
英文摘要：
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 $C^{1,1}$ realizations, in particular, stationary Gaussian fields, and obtain results which extend those known from the literature.
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