Electronic Journal of Probability

The Lower Envelope of Positive Self-Similar Markov Processes

Loic Chaumont and Juan Carlos Pardo Millan

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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 Dvoretzky and Erdos (1951), Motoo (1958), and Rivero (2003).

Article information

Electron. J. Probab., Volume 11 (2006), paper no. 49, 1321-1341.

Accepted: 17 December 2006
First available in Project Euclid: 31 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G18: Self-similar processes
Secondary: 60G51: Processes with independent increments; Lévy processes 60B10: Convergence of probability measures

Self-similar Markov process L'evy process Lamperti representation last passage time time reversal integral test law of the iterated logarithm

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Chaumont, Loic; Pardo Millan, Juan Carlos. The Lower Envelope of Positive Self-Similar Markov Processes. Electron. J. Probab. 11 (2006), paper no. 49, 1321--1341. doi:10.1214/EJP.v11-382. https://projecteuclid.org/euclid.ejp/1464730584

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