Cluster Random Fields and Random-Shift Representations

Enkelejd Hashorva ()
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Enkelejd Hashorva: University of Lausanne

Journal of Theoretical Probability, 2025, vol. 38, issue 3, 1-39

Abstract: Abstract 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.

Keywords: Cluster random fields; Random-shift representation; $$\alpha $$ α -homogeneous classes of random fields; Max-stable random fields; Extremal functionals; Rosiński representation; Lattices; 60G70; 60G60 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01420-1

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