Fractal Dimensions for Some Increments of the Uniform Empirical Process

Djamal Louani () and Alain Lucas
Additional contact information
Djamal Louani: Université de Paris 6
Alain Lucas: Université de Paris 6

Journal of Theoretical Probability, 2003, vol. 16, issue 1, 59-86

Abstract: Abstract In this paper, we investigate the limiting behavior of increments of the uniform empirical process. More precisely, we are concerned by sets of exceptional oscillation points related to large and small increments. We prove that these sets are random fractals and evaluate their Hausdorff dimensions. This work is a complement to the previous investigations carried out by Deheuvels and Mason(6) where Csörgő–Révész–Stute-type increments are studied.

Keywords: Exceptional oscillations; fractals; Hausdorff dimension; large increments; small increments; uniform empirical process (search for similar items in EconPapers)
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1022274303725 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:16:y:2003:i:1:d:10.1023_a:1022274303725

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

DOI: 10.1023/A:1022274303725

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 ().