Malti, Dounyazad Fatiha2019-12-182019-12-182019-10-24salle des thèsesDOC-519-09-01https://dspace.univ-tlemcen.dz/handle/112/15223We investigate the convergence of series of random variables with second exponential moments. We give sufficient conditions for the convergence of these series with respect to an exponential Orlicz norm and almost surely. Applying these results to sequences with dsubgaussian increments, we examine the asymptotic behavior of weighted sums of subgaussian random variables in a unified setting.frAlmost sure convergence, maximal inequalities, subgaussian random variables, exponential integrability, random series.Convergence presque sûre, inégalités maximales, variables aléatoires sous-gaussiennes, intégrabilité exponentielle, séries aléatoires.Thesis