Electronic Journal of Probability

The Lower Envelope of Positive Self-Similar Markov Processes

Loic Chaumont and Juan Carlos Pardo Millan

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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464730584

Digital Object Identifier
doi:10.1214/EJP.v11-382

Mathematical Reviews number (MathSciNet)
MR2268546

Zentralblatt MATH identifier
1127.60034

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

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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