Large deviations and Wschebor's theorems
We revisit Wschebor's theorems on small increments for processes with scaling and stationary properties and deduce large deviation principles.
math.PR↗
arXiv subjects
Jose R. Leon
Publications and source records attributed to Jose R. Leon.
Necessary and sufficient conditions for the finiteness of the second moment of the measure of level sets
For a smooth vectorial stationary Gaussian random field $X : Ω\times \mathbb{R}^d \to \mathbb{R}^d$, 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 $X : Ω\times \mathbb{R}^D \to \mathbb{R}^d$ with $D > d$.
math.PR↗