An Extension of the Class of Regularly Varying Functions

Meitner Cadena and Marie Kratz ()
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Meitner Cadena: UPMC - Université Pierre et Marie Curie - Paris 6, ESSEC Business School
Marie Kratz: ESSEC Business School, MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5 - UPD5 - Université Paris Descartes - Paris 5 - INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques - CNRS - Centre National de la Recherche Scientifique

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Abstract: We define a new class of positive and Lebesgue measurable functions in terms of their asymptotic behavior, which includes the class of regularly varying functions. We also characterize it by transformations, corresponding to generalized moments when these functions are random variables. We study the properties of this new class and discuss their applications to Extreme Value Theory.

Keywords: asymptotic behavior; measurable functions; Karamata's tauberian theorem; Karamata's theorem; Peter and Paul distribution; von Mises' conditions; extreme value theory; Karamata's representation theorem; regularly varying function; domains of attraction (search for similar items in EconPapers)
Date: 2014-12-14
Note: View the original document on HAL open archive server: https://essec.hal.science/hal-01097780
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