On the perimeter of excursion sets of shot noise random fields
نویسندگان
چکیده
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. AMS 2000 subject classifications: Primary 60G60, 60E10, 26B30, 28A75; secondary 60G10, 60F05, 60E07.
منابع مشابه
Central limit theorems for the excursion sets volumes of weakly dependent random fields
The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi–associated random fields on R are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the covariance matrix of the limiting distribution are provided. A statistical version of the CLT is considered as well. Some numerical results are also discussed. AMS 2000 subject ...
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