Malliavin Calculus and Self Normalized Sums

Solesne Bourguin (1) , Ciprian A. Tudor (2)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We study the self-normalized sums of independent random variables from the perspective of the Malliavin calculus. We give the chaotic expansion for them and we prove a Berry-Esséen bound with respect to several distances.

Domaines: Probabilités [math.PR]

Solesne Bourguin, Ciprian A. Tudor. Malliavin Calculus and Self Normalized Sums. 2011. ⟨hal-00605549⟩