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Strong mixing properties of max-infinitely divisible random fields

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  • Dombry, Clément
  • Eyi-Minko, Frédéric

Abstract

Let η=(η(t))t∈T be a sample continuous max-infinitely random field on a locally compact metric space T. For a closed subset S⊂T, we denote by ηS the restriction of η to S. We consider β(S1,S2), the absolute regularity coefficient between ηS1 and ηS2, where S1,S2 are two disjoint closed subsets of T. Our main result is a simple upper bound for β(S1,S2) involving the exponent measure μ of η: we prove that β(S1,S2)≤2∫P[η≮S1f,η≮S2f]μ(df), where f≮Sg means that there exists s∈S such that f(s)≥g(s).

Suggested Citation

  • Dombry, Clément & Eyi-Minko, Frédéric, 2012. "Strong mixing properties of max-infinitely divisible random fields," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3790-3811.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:11:p:3790-3811
    DOI: 10.1016/j.spa.2012.06.013
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    References listed on IDEAS

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    1. Kabluchko, Zakhar & Schlather, Martin, 2010. "Ergodic properties of max-infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 281-295, March.
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    Cited by:

    1. Davis, Richard A. & Mikosch, Thomas & Zhao, Yuwei, 2013. "Measures of serial extremal dependence and their estimation," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2575-2602.
    2. Koch, Erwan & Dombry, Clément & Robert, Christian Y., 2019. "A central limit theorem for functions of stationary max-stable random fields on Rd," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3406-3430.
    3. Damek, Ewa & Mikosch, Thomas & Zhao, Yuwei & Zienkiewicz, Jacek, 2023. "Whittle estimation based on the extremal spectral density of a heavy-tailed random field," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 232-267.
    4. Erwan Koch, 2019. "Spatial Risk Measures and Rate of Spatial Diversification," Risks, MDPI, vol. 7(2), pages 1-26, May.
    5. Richard A. Davis & Claudia Klüppelberg & Christina Steinkohl, 2013. "Statistical inference for max-stable processes in space and time," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 791-819, November.
    6. Brück, Florian, 2023. "Exact simulation of continuous max-id processes with applications to exchangeable max-id sequences," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    7. Das, Bikramjit & Engelke, Sebastian & Hashorva, Enkelejd, 2015. "Extremal behavior of squared Bessel processes attracted by the Brown–Resnick process," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 780-796.
    8. Erwan Koch, 2018. "Spatial risk measures and rate of spatial diversification," Papers 1803.07041, arXiv.org, revised Jun 2019.
    9. Yong Bum Cho & Richard A. Davis & Souvik Ghosh, 2016. "Asymptotic Properties of the Empirical Spatial Extremogram," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 757-773, September.
    10. Buhl, Sven & Klüppelberg, Claudia, 2018. "Limit theory for the empirical extremogram of random fields," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 2060-2082.

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