This book presents a broad overview of statistical modeling of extreme events along with the
most recent methodologies and various applications. It brings together background material …

Max-stable processes play an important role as models for spatial extreme events. Their
complex structure as the pointwise maximum over an infinite number of random functions …

Estimation of extreme value parameters from observations in the max-domain of attraction of
a multivariate max-stable distribution commonly uses aggregated data such as block …

Currently available models for spatial extremes suffer either from inflexibility in the
dependence structures that they can capture, lack of scalability to high dimensions, or in …

Peaks-over-threshold analysis using the generalised Pareto distribution is widely applied in
modelling tails of univariate random variables, but much information may be lost when …

Graphical models in extremes have emerged as a diverse and quickly expanding research
area in extremal dependence modeling. They allow for parsimonious statistical methodology …

Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They
are commonly defined as the limits of a sequence of expectations involving fractional …

A regularly varying time series as introduced in Basrak and Segers (2009) is a (multivariate)
time series such that all finite dimensional distributions are multivariate regularly varying …

Let X be a max-stable random vector with positive continuous density. It is proved that the
conditional independence of any collection of disjoint subvectors of X given the remaining …

The recent contribution (Dieker and Mikosch, 2015) obtained representations of max-stable
stationary Brown–Resnick process ζ Z (t), t∈ R d with spectral process Z being Gaussian …