Limit theorems and phase transitions for two models of summation of iid random variables depending on parameters (Q382190)

The paper considers the asymptotic distribution of the infinite summation of i.i.d. random variables which depend on two parameters. Various results are stated according to the different relations which may exist between these parameters and which are selected for their relevance in realistic physical systems. Two models are dealt with more precisely: namely models involving tempered heavy tails on the one hand, and models involving light tails with a heavy tailed input on the other hand.