The Annals of Probability

Laws of the Iterated Logarithm for Local Times of the Empirical Process

Richard F. Bass and Davar Khoshnevisan

Full-text: Open access

Abstract

We give exact expansions for the upper and lower tails of the distribution of the maximum of local time of standard Brownian bridge on interval [0, 1]. We use the above expansions to prove upper and lower laws of the iterated logarithm for the maximum of the local time of the uniform empirical process. This solves two open problems cited in the book of Shorack and Wellner.

Article information

Source
Ann. Probab., Volume 23, Number 1 (1995), 388-399.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988391

Digital Object Identifier
doi:10.1214/aop/1176988391

Mathematical Reviews number (MathSciNet)
MR1330775

Zentralblatt MATH identifier
0845.60079

JSTOR
links.jstor.org

Subjects
Primary: 60J55: Local time and additive functionals
Secondary: 62G30: Order statistics; empirical distribution functions 60J60: Diffusion processes [See also 58J65] 60J75: Jump processes

Keywords
Empirical process local times Brownian bridge laws of the iterated logarithm

Citation

Bass, Richard F.; Khoshnevisan, Davar. Laws of the Iterated Logarithm for Local Times of the Empirical Process. Ann. Probab. 23 (1995), no. 1, 388--399. doi:10.1214/aop/1176988391. https://projecteuclid.org/euclid.aop/1176988391


Export citation