Higher-order representation of Karamata theorem

Abstract

As an important result in extreme value theory, Karamata theorem provides the integral properties of regularly varying functions. In this paper, the third-order version of Karamata theorem is derived, which is generalization for the known Karamata theorem. Furthermore, analytic expressions for the second and third-order regularly varying function are established.

Keywords:

• Extreme value theory
• Karamata theorem
• regularly varying function
• third-order representation