The upper envelope of positive self-similar Markov processes
Abstract
We establish integral tests and laws of the iterated logarithm at 0 and at +∞, 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 Pa. These results extend integral test and laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erd\"os de and stable L\'evy processes conditioned to stay positive with no positive jumps due to Bertoin be1.
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