The classical modeling of spatial extremes relies on asymptotic models (ie, max‐stable or r‐
Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at …

Extreme Value Theory offers a careful, coherent exposition of the subject starting from the
probabilistic and mathematical foundations and proceeding to the statistical theory. The …

Stochastic geometry is a relatively new branch of mathematics. Although its predecessors
such as geometric probability date back to the 18th century, the formal concept of a random …

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 …

Abstract Models for stationary max-stable random fields are revisited and illustrated by two-
dimensional simulations. We introduce a new class of models, which are based on …

This book is concerned with extreme value theory for stochastic processes whose finite-
dimensional distributions are heavy-tailed in the restrictive sense of regular variation. These …

Let W i, i∈ ℕ, be independent copies of a zero-mean Gaussian process {W (t), t∈ ℝ d} with
stationary increments and variance σ 2 (t). Independently of W i, let∑ i= 1∞ δ U i be a …

We present properties of a dependence measure that arises in the study of extreme values
in multivariate and spatial problems. For multivariate problems the dependence measure …

This graduate-level textbook provides a straight-forward and mathematically rigorous
introduction to the standard theory of point processes. The author's aim is to present an …

(y+= max (y, 0)) where µ is a location parameter, ψ> 0 is a scale parameter and ξ is a shape
parameter. ξ→ 0 corresponds to the Gumbel distribution, ξ> 0 to the Fréchet distribution with …