2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111456We establish integral tests and laws of the iterated logarithm for the upper envelope of the future infimum of positive self-similar Markov processes and for increasing self-similar Markov processes at 0 and infinity. Our proofs are based on the Lamperti representation and time reversal arguments due to Chaumont and Pardo [9]. These results extend laws of the iterated logarithm for the future infimum of Bessel processes due to Khoshnevisan et al. [11].Probability60 G 18, 60 G 17, 60 G 51, 60 F 15text