# Asymptotic Properties of Ranked Heights in Brownian Excursions

E. Csáki, Yueyun Hu

Research output: Contribution to journalArticle

4 Citations (Scopus)

### Abstract

Pitman and Yor(20, 21) recently studied the distributions related to the ranked excursion heights of a Brownian bridge. In this paper, we study the asymptotic properties of the ranked heights of Brownian excursions. The heights of both high and low excursions are characterized by several integral tests and laws of the iterated logarithm. Our analysis relies on the distributions of the ranked excursion heights considered up to some random times.

Original language English 77-96 20 Journal of Theoretical Probability 14 1 https://doi.org/10.1023/A:1007868914766 Published - 2001

### Fingerprint

Brownian Excursion
Asymptotic Properties
Excursion
Integral Test
Brownian Bridge
Law of the Iterated Logarithm
Asymptotic properties

### Keywords

• Brownian and Bessel excursions
• Integral test
• Law of the iterated logarithm
• Ranked heights

### ASJC Scopus subject areas

• Mathematics(all)
• Statistics and Probability

### Cite this

In: Journal of Theoretical Probability, Vol. 14, No. 1, 2001, p. 77-96.

Research output: Contribution to journalArticle

@article{5cf11e76a0e545249a4695ac88e3f43e,
title = "Asymptotic Properties of Ranked Heights in Brownian Excursions",
abstract = "Pitman and Yor(20, 21) recently studied the distributions related to the ranked excursion heights of a Brownian bridge. In this paper, we study the asymptotic properties of the ranked heights of Brownian excursions. The heights of both high and low excursions are characterized by several integral tests and laws of the iterated logarithm. Our analysis relies on the distributions of the ranked excursion heights considered up to some random times.",
keywords = "Brownian and Bessel excursions, Integral test, Law of the iterated logarithm, Ranked heights",
author = "E. Cs{\'a}ki and Yueyun Hu",
year = "2001",
doi = "10.1023/A:1007868914766",
language = "English",
volume = "14",
pages = "77--96",
journal = "Journal of Theoretical Probability",
issn = "0894-9840",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - Asymptotic Properties of Ranked Heights in Brownian Excursions

AU - Csáki, E.

AU - Hu, Yueyun

PY - 2001

Y1 - 2001

N2 - Pitman and Yor(20, 21) recently studied the distributions related to the ranked excursion heights of a Brownian bridge. In this paper, we study the asymptotic properties of the ranked heights of Brownian excursions. The heights of both high and low excursions are characterized by several integral tests and laws of the iterated logarithm. Our analysis relies on the distributions of the ranked excursion heights considered up to some random times.

AB - Pitman and Yor(20, 21) recently studied the distributions related to the ranked excursion heights of a Brownian bridge. In this paper, we study the asymptotic properties of the ranked heights of Brownian excursions. The heights of both high and low excursions are characterized by several integral tests and laws of the iterated logarithm. Our analysis relies on the distributions of the ranked excursion heights considered up to some random times.

KW - Brownian and Bessel excursions

KW - Integral test

KW - Law of the iterated logarithm

KW - Ranked heights

UR - http://www.scopus.com/inward/record.url?scp=0035611968&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035611968&partnerID=8YFLogxK

U2 - 10.1023/A:1007868914766

DO - 10.1023/A:1007868914766

M3 - Article

AN - SCOPUS:0035611968

VL - 14

SP - 77

EP - 96

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 1

ER -