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January 2016 On the perimeter of excursion sets of shot noise random fields
Hermine Biermé, Agnès Desolneux
Ann. Probab. 44(1): 521-543 (January 2016). DOI: 10.1214/14-AOP980

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.

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Hermine Biermé. Agnès Desolneux. "On the perimeter of excursion sets of shot noise random fields." Ann. Probab. 44 (1) 521 - 543, January 2016. https://doi.org/10.1214/14-AOP980

Information

Received: 1 October 2013; Revised: 1 July 2014; Published: January 2016
First available in Project Euclid: 2 February 2016

zbMATH: 1343.60060
MathSciNet: MR3457393
Digital Object Identifier: 10.1214/14-AOP980

Subjects:
Primary: 26B30, 28A75, 60E10, 60G60
Secondary: 60E07, 60F05, 60G10

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 1 • January 2016
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