An extension of the class of regularly varying functions

TL;DR

This paper introduces a new class of functions extending regularly varying functions, characterized by their asymptotic behavior and transformations, with applications to Extreme Value Theory.

Contribution

It defines and studies a new class of functions that generalize regularly varying functions, providing insights into their properties and applications.

Findings

Includes the class of regularly varying functions

Characterizes the new class via transformations

Discusses applications to Extreme Value Theory

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.