On the perimeter of excursion sets of shot noise random fields

Biermé, Hermine ^[1] ; Desolneux, Agnès ^[2]
1. [1] University of Poitiers
  
  University of Poitiers
  
  Arrondissement de Poitiers, Francia
2. [2] École Normale Supérieure de Cachan
  
  École Normale Supérieure de Cachan
  
  Arrondissement de L'Haÿ-les-Roses, Francia
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 1, 2016, págs. 521-543
Idioma: inglés
DOI: 10.1214/14-AOP980
Enlaces
- Texto completo
Resumen
- 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.