A timely and comprehensive treatment of random field theory with applications across
diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses …

Since the publication of the first edition of this seminar book in 1994, the theory and
applications of extremes and rare events have enjoyed an enormous and still increasing …

We study the Euler characteristic of an excursion set of a stationary isotropic Gaussian
random field X:Ω*R^d→R. Let us fix a level u∈R and let us consider the excursion set …

This paper presents a synthesis on the mathematical work done on level crossings of
stationary Gaussian processes, with some extensions. The main results [(factorial) moments …

For a smooth stationary Gaussian field f on R d and level ℓ∈ R, we consider the number of
connected components of the excursion set {f≥ ℓ}(or level set {f= ℓ}) contained in large …

Our interest in this paper is to explore limit theorems for various geometric functionals of
excursion sets of isotropic Gaussian random fields. In the past, asymptotics of nonlinear …

In the present paper, we deal with a stationary isotropic random field X:R^d→R and we
assume it is partially observed through some level functionals. We aim at providing a …

We study the number of points where the gradient of a stationary Gaussian random field
restricted to a compact set in R d takes a fixed value. We extend to higher dimensions the …

We propose a scheme for finding the probabilities of events related to crossings of a level by
a random process. Using this scheme, we estimate the probability that the first achievement …

We study the variance of the number of zeroes of a stationary Gaussian process on a long
interval. We give a simple asymptotic description under mild mixing conditions. This allows …