The Annals of Probability

On the Fractal Nature of Empirical Increments

Paul Deheuvels and David M. Mason

Full-text: Open access

Abstract

We prove that the set of points where exceptional oscillations of empirical and related processes occur infinitely often is a random fractal, and evaluate its Hausdorff dimension.

Article information

Source
Ann. Probab., Volume 23, Number 1 (1995), 355-387.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988390

Digital Object Identifier
doi:10.1214/aop/1176988390

Mathematical Reviews number (MathSciNet)
MR1330774

Zentralblatt MATH identifier
0835.60024

JSTOR
links.jstor.org

Subjects
Primary: 60F06
Secondary: 60F15: Strong theorems

Keywords
Empirical processes fractals strong laws functional laws of the iterated logarithm tail and local empirical processes

Citation

Deheuvels, Paul; Mason, David M. On the Fractal Nature of Empirical Increments. Ann. Probab. 23 (1995), no. 1, 355--387. doi:10.1214/aop/1176988390. https://projecteuclid.org/euclid.aop/1176988390


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