Necessary and sufficient conditions for the finiteness of the second moment of the measure of level sets

Autor:	Azais, J-M, Leon, Jose R.
Rok vydání:	2019
Předmět:	Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	For a smooth vectorial stationary Gaussian random field $X : \Omega \times \mathbb{R}^d \to \mathbb{R}^d$, we give necessary and sufficient conditions to have a finite second moment for the number of roots of $X(t) - u$. The results are obtained by using a method of proof inspired on the one obtained by D. Geman for stationary Gaussian processes long time ago. Afterwards the same method is applied to the number of critical points of a scalar random field and also to the level set of a vectorial process $X : \Omega \times \mathbb{R}^D \to \mathbb{R}^d$ with $D > d$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.12342 Zobrazit plný text záznamu View this record from Arxiv