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Multivariate max-stable processes and homogeneous functionals

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  • Hashorva, Enkelejd
  • Kume, Alfred

Abstract

Multivariate max-stable processes are important for both theoretical investigations and various statistical applications motivated by the fact that these are limiting processes, for instance of stationary multivariate regularly varying time series, (Dombry et al., 2018). In this contribution we explore the relation between homogeneous functionals and multivariate max-stable processes and discuss the connections between multivariate max-stable process and zonoid/max-zonoid equivalence. We illustrate our results considering Brown–Resnick and Smith processes.

Suggested Citation

  • Hashorva, Enkelejd & Kume, Alfred, 2021. "Multivariate max-stable processes and homogeneous functionals," Statistics & Probability Letters, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:stapro:v:173:y:2021:i:c:s0167715221000286
    DOI: 10.1016/j.spl.2021.109066
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    References listed on IDEAS

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    1. Molchanov, Ilya & Stucki, Kaspar, 2013. "Stationarity of multivariate particle systems," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2272-2285.
    2. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    3. Dombry, Clément & Kabluchko, Zakhar, 2017. "Ergodic decompositions of stationary max-stable processes in terms of their spectral functions," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1763-1784.
    4. Wu, Lifan & Samorodnitsky, Gennady, 2020. "Regularly varying random fields," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4470-4492.
    5. Marc G. Genton & Simone A. Padoan & Huiyan Sang, 2015. "Multivariate max-stable spatial processes," Biometrika, Biometrika Trust, vol. 102(1), pages 215-230.
    6. Wang, Yizao & Stoev, Stilian A., 2010. "On the association of sum- and max-stable processes," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 480-488, March.
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