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

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