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The lower envelope of positive self-similar Markov processes

Loïc Chaumont·Juan-Carlos Pardo
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Abstract

We establish integral tests and laws of the iterated logarithm for the lower envelope of positive self-similar Markov processes at 0 and $+\infty$. Our proofs are based on the Lamperti representation and time reversal arguments. These results extend laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erd\"{o}s, Motoo and Rivero.

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Loïc Chaumont, Juan-Carlos Pardo. 2006-01-09. The lower envelope of positive self-similar Markov processes. https://arxiv.org/abs/math/0601177

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