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Cluster Random Fields and Random-Shift Representations

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  • Enkelejd Hashorva

    (University of Lausanne)

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.

Suggested Citation

  • Enkelejd Hashorva, 2025. "Cluster Random Fields and Random-Shift Representations," Journal of Theoretical Probability, Springer, vol. 38(3), pages 1-39, September.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:3:d:10.1007_s10959-025-01420-1
    DOI: 10.1007/s10959-025-01420-1
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    References listed on IDEAS

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