Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 24 (2019), paper no. 17, 8 pp.
Conditions for the finiteness of the moments of the volume of level sets
Let $X(t)$ be a Gaussian random field $\mathbb R^d\to \mathbb R$. Using the notion of $(d-1)$-integral geometric measures, we establish a relation between (a) the volume of level sets, and (b) the number of crossings of the restriction of the random field to a line. Using this relation we prove the equivalence between the finiteness of the expectation and the finiteness of the second spectral moment matrix. Sufficient conditions for finiteness of higher moments are also established.
Electron. Commun. Probab., Volume 24 (2019), paper no. 17, 8 pp.
Received: 1 November 2018
Accepted: 25 January 2019
First available in Project Euclid: 22 March 2019
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Armentano, D.; Azaïs, J-M.; Ginsbourger, D.; León, J.R. Conditions for the finiteness of the moments of the volume of level sets. Electron. Commun. Probab. 24 (2019), paper no. 17, 8 pp. doi:10.1214/19-ECP214. https://projecteuclid.org/euclid.ecp/1553220033