ON THE CAPACITY FUNCTIONAL OF EXCURSION SETS OF GAUSSIAN RANDOM FIELDS ON R2

被引：1

作者：

Kratz, Marie ^{[1
,2
]}

Nagel, Werner ^{[3
]}

机构：

[1] ESSEC Business Sch, Ave Bernard Hirsch BP 50105, F-95021 Cergy Pontoise, France

[2] Univ Paris 05, MAP5, Paris, France

[3] Friedrich Schiller Univ Jena, Fak Math & Informat, D-07737 Jena, Germany

来源：

ADVANCES IN APPLIED PROBABILITY | 2016年 / 48卷 / 03期

关键词：

Capacity functional; crossings; excursion set; Gaussian field; growing circle method; Rice formula; second moment measure; sweeping line method; stereology; stochastic geometry;

D O I：

10.1017/apr.2016.24

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

When a random field (X-t, t is an element of R-2) is thresholded on a given level u, the excursion set is given by its indicator 1([u), (infinity)) (X-t). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets as, e.g. the capacity functional as well as the second moment measure of the boundary length. It extends results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossings theory, in particular, Rice methods, and from integral and stochastic geometry.

引用

页码：712 / 725

页数：14

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