Transformations des lois multivari\'ees avec queues r\'eguli\`eres

TL;DR

This paper investigates how certain transformations of multivariate regularly varying vectors affect their tail properties, providing conditions under which regular variation is preserved.

Contribution

It introduces sufficient conditions for preserving regular variation under specific transformations of multivariate vectors with regular tails.

Findings

Identifies conditions that maintain regular variation after transformations.

Provides theoretical results on tail behavior preservation.

Enhances understanding of multivariate tail transformations.

Abstract

Let $X$ be a random vector in $\rd$ with a regularly varying tail. We consider two transformations $\|X\|f(\frac{X}{\|X\|})$, $f: \sd\to\sd$, and $Xf(\frac{X}{\|X\|})$, $f: \sd\to \mathbb{R}_+$. Some sufficient conditions for preserving the property of regularity of the tail for this kind of transformations are given.