2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125071We establish integral tests and laws of the iterated logarithm at 0 and at $+\infty$, for the upper envelope of positive self-similar Markov processes. Our arguments are based on the Lamperti representation, time reversal arguments and on the study of the upper envelope of their future infimum due to Pardo \cite{Pa}. These results extend integral test and laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erdös \cite{de} and stable Lévy processes conditioned to stay positive with no positive jumps due to Bertoin \cite{be1}.Probability60 G 18, 60 G 17, 60 G 51, 60 F 15text