Transformations of multivariate regularly varying tail distributions

Youri Davydov (1) , Shuyan Liu (2, 3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA)
3 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

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.

Mots clés: regular variation; multivariate stable distributions; spectral measure

Domaines: Probabilités [math.PR]

Youri Davydov, Shuyan Liu. Transformations of multivariate regularly varying tail distributions. Revue roumaine de mathématiques pures et appliquées, 2010, 55 (6), pp.483-492. ⟨hal-00519735⟩