"Asymptotic properties of ranked heights in Brownian excursions"

Endre Csáki and Yueyun Hu

Summary: Pitman and Yor 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: Ranked heights, Brownian and Bessel excursions, integral test, law of the iterated logarithm.

AMS 1991 subject classification: 60F15, 60G55.