The upper envelope of positive self-similar Markov processes
Probability
2007-05-23 v1
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 \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}.
Keywords
Cite
@article{arxiv.math/0703071,
title = {The upper envelope of positive self-similar Markov processes},
author = {Juan Carlos Pardo Millan},
journal= {arXiv preprint arXiv:math/0703071},
year = {2007}
}