论文标题
群集随机字段和随机移动表示
Cluster Random Fields and Random-Shift Representations
论文作者
论文摘要
簇随机场（CRF）在固定固定的常规随机场（RF）的极端研究中起着至关重要的作用。特别是，它们出现在Max-stable和$α$稳定的RFS的Rosiński代表中。在这项贡献中，我们在抽象环境中引入CRF，证明它们对于$α$均匀的RFS的换档生成类至关重要。此外，我们研究了CRF，Tail RFS}和频谱尾RF之间的关系。此贡献中讨论的应用包括极端功能指数的新表示和纯粹的耗散最大稳定RF。
Cluster random fields (CRFs) play a crucial role in the study of extremes of stationary regularly varying random fields (RFs). In particular, they appear in the Rosiński representation of max-stable and $α$-stable RFs. In this contribution we introduce CRFs in an abstract setting proving that they are crucial for the construction of shift-generated classes of $α$-homogeneous RFs. Further, we investigate the relations between CRFs, tail RFs} and spectral tail RFs. Applications discussed in this contribution include new representations of extremal functional indices and purely dissipative max-stable RFs.
