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Multilevel clustering of extremes

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  • Novak, S. Y.

Abstract

We investigate asymptotic properties of two-dimensional empirical point processes of exceedances (EPPE). We give an alternative description of the class of possible limit laws. Necessary and sufficient conditions for the weak convergence of one-dimensional EPPEs and complete convergence of two-dimensional EPPEs are established.

Suggested Citation

  • Novak, S. Y., 2002. "Multilevel clustering of extremes," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 59-75, January.
    • Handle: RePEc:eee:spapps:v:97:y:2002:i:1:p:59-75
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    References listed on IDEAS

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    1. Hsing, Tailen, 1988. "On the extreme order statistics for a stationary sequence," Stochastic Processes and their Applications, Elsevier, vol. 29(1), pages 155-169.
    2. Hsing, Tailen, 1987. "On the characterization of certain point processes," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 297-316.
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    Cited by:

    1. Novak, S.Y. & Xia, A., 2012. "On exceedances of high levels," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 582-599.
    2. Hashorva, Enkelejd, 2007. "On the asymptotic distribution of certain bivariate reinsurance treaties," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 200-208, March.
    3. Segers, J.J.J., 2006. "Rare Events, Temporal Dependence and the Extremal Index," Discussion Paper 2006-7, Tilburg University, Center for Economic Research.
    4. Segers, J.J.J., 2006. "Rare Events, Temporal Dependence and the Extremal Index," Other publications TiSEM 04952d0f-2b24-44ad-bf07-f, Tilburg University, School of Economics and Management.
    5. Hashorva, Enkelejd, 2003. "On the number of near-maximum insurance claim under dependence," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 37-49, February.

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