  We 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].
