Scholarlink

<p>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 <i>Rosiński representation</i> of max-stable and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10959_2025_1420_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-stable RFs. In this contribution we introduce CRFs in an abstract setting proving that they are crucial for the construction of <i>shift-generated</i> classes of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10959_2025_1420_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-homogeneous RFs. Further, we investigate the relations between CRFs, <i>tail RFs</i> and <i>spectral tail RFs</i>. Applications discussed in this contribution include new representations of extremal functional indices and purely dissipative max-stable RFs.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Cluster Random Fields and Random-Shift Representations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月21日

查看全文
  • Enkelejd Hashorva

摘要

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 \(\alpha \) 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 \(\alpha \) 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.