The upper envelope of positive self-similar Markov processes

Details The upper envelope of positive self-similar Markov processes The upper envelope of positive self-similar Markov processes

2007-03-02

arxiv.org/abs/math/0703071v1

Mathematics

Probability

Scientific paper

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 Erd\"os \cite{de} and stable L\'evy processes conditioned to stay positive with no positive jumps due to Bertoin \cite{be1}.

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