ON THE PERIMETER OF EXCURSION SETS OF SHOT NOISE RANDOM FIELDS

被引：14

作者：

Bierme, Hermine ^{[1
]}

Desolneux, Agnes ^{[2
]}

机构：

[1] Univ Poitiers, CNRS, UMR 7348, LMA, Teleport 2-BP30179,Blvd Marie & Pierre Curie, F-86962 Chasseneuil, France

[2] Ecole Normale Super, CNRS, CMLA, UMR 8536, 61 Ave President Wilson, F-94235 Cachan, France

来源：

ANNALS OF PROBABILITY | 2016年 / 44卷 / 01期

关键词：

Shot noise; excursion set; stationary process; Poisson process; characteristic function; functions of bounded variation; coarea formula; LEVEL-CROSSINGS; RICE FORMULA;

D O I：

10.1214/14-AOP980

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：

In this paper, we use the framework of functions of bounded variation and the coarea formula to give an explicit computation for the expectation of the perimeter of excursion sets of shot noise random fields in dimension n >= 1. This will then allow us to derive the asymptotic behavior of these mean perimeters as the intensity of the underlying homogeneous Poisson point process goes to infinity. In particular, we show that two cases occur: we have a Gaussian asymptotic behavior when the kernel function of the shot noise has no jump part, whereas the asymptotic is non-Gaussian when there are jumps.

引用

页码：521 / 543

页数：23

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