Open Access
Translator Disclaimer
May, 1983 A Conditioned Limit Theorem for Random Walk and Brownian Local Time on Square Root Boundaries
Priscilla Greenwood, Edwin Perkins
Ann. Probab. 11(2): 227-261 (May, 1983). DOI: 10.1214/aop/1176993594

Abstract

We count the number of times a random walk exits from a square root boundary and show that the normalized counting process and the normalized random walk converge jointly in law to a "local time," whose inverse is a stable subordinator of a known index, and a Brownian motion. The study of this limit process leads to some precise sample path properties of Brownian motion. These properties improve earlier results of Dvoretsky and Kahane on the existence of small oscillations in the Brownian path.

Citation

Download Citation

Priscilla Greenwood. Edwin Perkins. "A Conditioned Limit Theorem for Random Walk and Brownian Local Time on Square Root Boundaries." Ann. Probab. 11 (2) 227 - 261, May, 1983. https://doi.org/10.1214/aop/1176993594

Information

Published: May, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0522.60030
MathSciNet: MR690126
Digital Object Identifier: 10.1214/aop/1176993594

Subjects:
Primary: 60F17
Secondary: 26E35 , 60G17 , 60J55 , 60J65 , 60K05

Keywords: Brownian motion , domain of attraction , Local time , Random walk , Regenerative set , square root boundary , stable subordinator , Weak invariance principle

Rights: Copyright © 1983 Institute of Mathematical Statistics

JOURNAL ARTICLE
35 PAGES


SHARE
Vol.11 • No. 2 • May, 1983
Back to Top