标题： 基于单个极端事件的极值稳定过程的表示 显示英文标题

标题： Representations of max-stable processes based on single extreme events

摘要： 本文为在一般空间上具有某种增量表示的极值稳定过程 \xi 的新推断方法提供了基础，该表示在重要情况下比极值稳定过程本身具有更简单的结构。 相应的超过阈值方法将包括所有在某种意义上极端的单个事件，因此与基于块最大值的估计程序相比，将依赖于数量显著更大的数据。 对属于 \xi 极值域的 \eta 过程进行条件化，证明了 \eta 增量的几个收敛结果。 以类似的方式，可以从适当条件化的单个事件 \eta 中提取混合移动最大值（M3）过程的形状函数。 将这两种方法联系起来，确定了同时具有增量表示和 M3 表示的过程的转换公式。 显示英文摘要

摘要： This paper provides the basis for new methods of inference for max-stable processes \xi\ on general spaces that admit a certain incremental representation, which, in important cases, has a much simpler structure than the max-stable process itself. A corresponding peaks-over-threshold approach will incorporate all single events that are extreme in some sense and will therefore rely on a substantially larger amount of data in comparison to estimation procedures based on block maxima. Conditioning a process \eta\ in the max-domain of attraction of \xi\ on being extremal, several convergence results for the increments of \eta\ are proved. In a similar way, the shape functions of mixed moving maxima (M3) processes can be extracted from suitably conditioned single events \eta. Connecting the two approaches, transformation formulae for processes that admit both an incremental and an M3 representation are identified.