UMR 5584

# Large deviations for sums of independent random variables and martingales

### Mercredi 22 mars 10:30-11:30 - Liu Quansheng - Université de Bretagne-sud

Large deviations for sums of independent random variables and martingales

Résumé : In this talk, I will present some recent results about large deviations on sums of independent random variables and martingales. In particular, I will show an improvement of the classical Beinstein – Cramér - Chernoff bound on large deviations for sums of independent random variables by adding a missing factor ; this result extends Talagrand’s inequality (1995) about the missing factor in Hoeffding’s inequality to non-bounded variables, and improves Talagrand’s inequality to an equality which leads to large deviation expansions similar to those of Cramér (1938), Bahadur-Rao (1960) and Sakhanenko (1991). Large deviation results on martingales, such as exponential and sub-exponential bounds are also presented. (Based on joint work with Xiequan Fan and Ion Grama.)

Pour en savoir plus sur cet événement, consultez l'article Séminaires SPOC