The lower envelope of positive self-similar Markov processes

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

2006-01-09

arxiv.org/abs/math/0601177v1

Mathematics

Probability

Scientific paper

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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