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The upper envelope of positive self-similar Markov processes

Juan Carlos Pardo Millan
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Abstract

We 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}.

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Juan Carlos Pardo Millan. 2007-03-02. The upper envelope of positive self-similar Markov processes. https://arxiv.org/abs/math/0703071

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