Related papers: Conditioned limit laws for inverted max-stable pro…
Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…
The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable processes or $r$-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often…
In recent years, parametric models for max-stable processes have become a popular choice for modeling spatial extremes because they arise as the asymptotic limit of rescaled maxima of independent and identically distributed random…
Environmental data science for spatial extremes has traditionally relied heavily on max-stable processes. Even though the popularity of these models has perhaps peaked with statisticians, they are still perceived and considered as the…
Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…
Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…
Since many environmental processes such as heat waves or precipitation are spatial in extent, it is likely that a single extreme event affects several locations and the areal modelling of extremes is therefore essential if the spatial…
Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit of…
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 makes simulation highly nontrivial. Algorithms based on finite…
Let $X_{i,n},n\in \mathbb{N},1\leq i\leq n$, be a triangular array of independent $\mathbb{R}^d$-valued Gaussian random vectors with correlation matrices $\Sigma_{i,n}$. We give necessary conditions under which the row-wise maxima converge…
Since many environmental processes such as heat waves or precipitation are spatial in extent, it is likely that a single extreme event affects several locations and the areal modeling of extremes is therefore essential if the spatial…
Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models…
Recently the regular conditional distributions of max-infinitely divisible processes were derived by \citet{Dombry2011} and although these conditional distributions have complicated closed forms, \citet{Dombry2011b} introduce an algorithm…
Being the max-analogue of $\alpha$-stable stochastic processes, max-stable processes form one of the fundamental classes of stochastic processes. With the arrival of sufficient computational capabilities, they have become a benchmark in the…
We consider the class of simple Brown-Resnick max-stable processes whose spectral processes are continuous exponential martingales. We develop the asymptotic theory for the realized power variations of these max-stable processes, that is,…
For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max-stable models are inadequate to capture the rate of joint tail decay,…