"Invariance Principles for Ranked Excursion Lengths and Heights"

Endre Csáki and Yueyun Hu

Summary: In this note we prove strong invariance principles between ranked excursion lengths and heights of a simple random walk and those of a standard Brownian motion. Some consequences concerning limiting distributions and strong limit theorems will also be presented.

Keywords: excursion lengths, excursion heights, invariance principle.

AMS 2000 subject classification: 60F17, 60F05, 60F15.