When passing from the univariate to the multivariate setting, modelling extremes becomes much more intricate. In this introductory exposition, classical multivariate extreme value theory is presented from the point of view of multivariate excesses over high thresholds as modelled by the family of multivariate generalized Pareto distributions. The formulation in terms of failure sets in the sample space intersecting the sample cloud leads to the over-arching perspective of point processes. Max-stable or generalized extreme value distributions are finally obtained as limits of vectors of componentwise maxima by considering the event that a certain region of the sample space does not contain any observation.

翻译：当从单变量情形过渡到多变量情形时，极端值的建模变得更为复杂。在这篇介绍性论述中，经典多元极值理论是从超越高阈值的多元超限角度进行阐述的，其建模基于多元广义帕累托分布族。通过样本空间中与样本云相交的失效集表述，引出了点过程的总体视角。最后，通过考虑样本空间特定区域内不包含任何观测值的事件，将分量最大值向量取极限，得到了最大稳定分布或广义极值分布。