Conditions for the finiteness of the moments of the volume of level sets

Let X(t) be a Gaussian random field R d → 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 t...

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Bibliographic Details

Main Author:	Armentano, Diego (author)
Other Authors:	Azaïs, J.M. (author), Ginsbourger, D. (author), León, José Rafael (author)
Format:	article
Language:	English
Published:	2019
Subjects:	Gaussian fields Nodal sets Crofton formula Kac-Rice formula
Online Access:	https://hdl.handle.net/20.500.12008/28107
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