Bernou, Ismahen2023-05-282023-05-282022-12-03salle des thèsesDoct LMD Maths-519-15-01https://dspace.univ-tlemcen.dz/handle/112/20612In this thesis, we are interested in the asymptotic behavior of a class of stochastic processes with d-Φ-subgaussian increments and weighted sums of random variables with infinite means. For the first family of processes, the Dudley metric entropy criterion is used to establish a law of iterated logarithm. For the second family, a weak law of large numbers is proved in a unified framework under weak dependence conditions. A necessary condition for the validity of this law is also derivedfr: law of the iterated logarithm, metric entropy, Φ-sub-gaussian, Weak laws, Weighted exact laws, Pareto-type distributions, Rosenthal–type maximal inequalities, St. Petersburg game, Feller gameloi du logarithme itéré, nombre d’entropie, Φ-sous-gaussien, lois faibles, lois exactes pondérées, distribution de type Pareto, inégalités maximales de type Rosenthal, jeu de St. Petersburg, jeu de Feller.Thesis