Asymptotic convergence of the extremes of a geometric random variables sequence

---

Résumé

In this paper, we give some contributions to the analysis of the behavior of the extremes of a category of random variables (r.v.) of geometric type. First, we exhibit a subsequence making certain r.v. of integer part converge. Then we prove the convergence in law of extremes of a sequence of geometric type r.v. Finally, we prove the mean convergence of the extremes of a sequence of geometric type r.v.

Mots-clés

geometric random variable, asymptotic law of extremes, convergent subsequence, functional convergence.