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Equivalence classes of regularly varying functions

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  • De Haan, Laurens

Abstract

A useful method to derive limit results for partial maxima and record values of independent, identically distributed random variables is to start from one specific probability distribution and to extend the result for this distribution to a class of distributions.This method involves an extended theory of regularly varying functions. In this paper, equivalence classes of regularly varying functions (in the extended sense) are studied, which is relevant to the problems mentioned above.

Suggested Citation

  • De Haan, Laurens, 1974. "Equivalence classes of regularly varying functions," Stochastic Processes and their Applications, Elsevier, vol. 2(3), pages 243-259, July.
    • Handle: RePEc:eee:spapps:v:2:y:1974:i:3:p:243-259
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    Cited by:

    1. de Haan, L. & Resnick, S. I., 1979. "Local Limit Theorems for Sample Extremes," Econometric Institute Archives 272194, Erasmus University Rotterdam.
    2. Ipsen, Yuguang & Maller, Ross & Resnick, Sidney, 2020. "Trimmed Lévy processes and their extremal components," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2228-2249.
    3. A. Berlinet & A. Elamine & A. Mas, 2011. "Local linear regression for functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 1047-1075, October.
    4. Omey, Edward & Segers, Johan, 2009. "Generalised regular variation of arbitrary order," Working Papers 2009/02, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    5. Saulius Paukštys & Jonas Šiaulys & Remigijus Leipus, 2023. "Truncated Moments for Heavy-Tailed and Related Distribution Classes," Mathematics, MDPI, vol. 11(9), pages 1-15, May.

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