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2020 Necessary and sufficient conditions for the finiteness of the second moment of the measure of level sets
Jean-Marc Azaïs, José R. León
Electron. J. Probab. 25: 1-15 (2020). DOI: 10.1214/20-EJP508

Abstract

For a smooth vectorial stationary Gaussian random field, $X:\Omega \times \mathbb {R}^{d}\to \mathbb {R}^{d}$, we provided necessary conditions to have a finite second moment for the number of roots of $X(t)-u$. Then, under a more restrictive hypothesis, some sufficient conditions were also given. The results were obtained using a method of proof inspired the one obtained by D. Geman for stationary Gaussian processes. Afterward, the same method is applied to the number of critical points of a scalar random field and to the level set of a vectorial process, $X:\Omega \times \mathbb {R}^{D}\to \mathbb {R}^{d}$, with $D>d$.

Citation

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Jean-Marc Azaïs. José R. León. "Necessary and sufficient conditions for the finiteness of the second moment of the measure of level sets." Electron. J. Probab. 25 1 - 15, 2020. https://doi.org/10.1214/20-EJP508

Information

Received: 17 June 2019; Accepted: 10 August 2020; Published: 2020
First available in Project Euclid: 8 September 2020

zbMATH: 07252701
Digital Object Identifier: 10.1214/20-EJP508

Subjects:
Primary: 60G15, 60G60

JOURNAL ARTICLE
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