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Study of the perimeter of a shot noise random field by an elementary approach

Abstract : The study of the geometry of excursion sets of 2D random fields, especially the perimeter or length of level lines, has a growing interest from both the theoretical developments and the statistical applications. In this paper we are interested in the relationship between the perimeter of the excursion sets of a shot noise random field compared to the well known Gaussian framework. Our approach follows the weak framework of special bounded variation functions in which we consider the functions that map the level of the excursion set to the perimeter of the excursion set. In this unified framework we exhibit two different regimes with respect to the intensity of the shot noise random field. The first one is the classical Gaussian regime in high intensity, while the second new one, in low intensity, is related to an elementary approximation. In the explicit case of Gaussian correlation functions, we show the pertinence of such approximation for statistical evaluation. At least, this enables us to propose a classification procedure to discriminate Gaussian or shot noise fields.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03627051
Contributor : Hermine Biermé Connect in order to contact the contributor
Submitted on : Friday, April 1, 2022 - 8:49:42 AM
Last modification on : Thursday, April 7, 2022 - 3:34:10 AM
Long-term archiving on: : Saturday, July 2, 2022 - 6:20:34 PM

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  • HAL Id : hal-03627051, version 1

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Hermine Biermé, Antoine Lerbet. Study of the perimeter of a shot noise random field by an elementary approach. 2022. ⟨hal-03627051⟩

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