2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173983We propose several exponential inequalities for self-normalized martingales similar to those established by De la Peña. The keystone is the introduction of a new notion of random variable heavy on left or right. Applications associated with linear regressions, autoregressive and branching processes are also provided.Published in at http://dx.doi.org/10.1214/07-AAP506 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics TheoryProbability60E15, 60G42 (Primary) 60G15, 60J80 (Secondary)text