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Semicontinuous processes in multi-dimensional extreme value theory

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  • Norberg, Tommy

Abstract

The structure of the large values attained by a stationary random process indexed by a one-dimensional parameter is well described in the literature in many cases of interest. Here this structure is described in terms of semicontinuous processes. The main advantage with this is that it automatically generalizes to processes with multi-dimensional parameter. Concrete asymptotic results are given for Gaussian fields, which, in case of continuous parameter, may possess very erratic sample paths.

Suggested Citation

  • Norberg, Tommy, 1987. "Semicontinuous processes in multi-dimensional extreme value theory," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 27-55.
    • Handle: RePEc:eee:spapps:v:25:y:1987:i::p:27-55
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    Cited by:

    1. Terán, Pedro & López-Díaz, Miguel, 2014. "Strong consistency and rates of convergence for a random estimator of a fuzzy set," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 130-145.
    2. Sabourin, Anne & Segers, Johan, 2016. "Marginal standardization of upper semicontinuous processes with application to max-stable processes," LIDAM Discussion Papers ISBA 2016019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Giovanni Paolo Crespi & Elisa Mastrogiacomo, 2020. "Qualitative robustness of set-valued value-at-risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 25-54, February.

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