The Upper Envelope of Positive Self-Similar Markov Processes

J. C. Pardo ()
Additional contact information
J. C. Pardo: Université Pierre et Marie Curie

Journal of Theoretical Probability, 2009, vol. 22, issue 2, 514-542

Abstract: Abstract We establish integral tests in connection with 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 and on the study of the upper envelope of the future infimum due to the author (see Pardo in Stoch. Stoch. Rep. 78:123–155, [2006]). These results extend laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erdős (Proceedings of the Second Berkeley Symposium, [1951]) and stable Lévy processes with no positive jumps conditioned to stay positive due to Bertoin (Stoch. Process. Appl. 55:91–100, [1995]).

Keywords: Self-similar Markov process; Self-similar additive processes; Future infimum process; Lévy process; Lamperti representation; First and last passage time; Integral test; Law of the iterated logarithm; 60G18; 60G17; 60G51; 60F15 (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-008-0152-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:22:y:2009:i:2:d:10.1007_s10959-008-0152-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-008-0152-z

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().