## The Annals of Probability

### On the perimeter of excursion sets of shot noise random fields

#### Abstract

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 $n\geq1$. 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.

#### Article information

Source
Ann. Probab., Volume 44, Number 1 (2016), 521-543.

Dates
Received: October 2013
Revised: July 2014
First available in Project Euclid: 2 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1454423048

Digital Object Identifier
doi:10.1214/14-AOP980

Mathematical Reviews number (MathSciNet)
MR3457393

Zentralblatt MATH identifier
1343.60060

#### Citation

Biermé, Hermine; Desolneux, Agnès. On the perimeter of excursion sets of shot noise random fields. Ann. Probab. 44 (2016), no. 1, 521--543. doi:10.1214/14-AOP980. https://projecteuclid.org/euclid.aop/1454423048

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