## Electronic Journal of Probability

### The Lower Envelope of Positive Self-Similar Markov Processes

#### 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

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

Rights

#### 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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