Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


On the global asymptotic behavior of Brownian local time on the circle

Author: E. Bolthausen
Journal: Trans. Amer. Math. Soc. 253 (1979), 317-328
MSC: Primary 60F05; Secondary 60J55
MathSciNet review: 536950
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The asymptotic behavior of the local time of Brownian motion on the circle is investigated. For fixed time point t this is a (random) continuous function on $ {S^1}$. It is shown that after appropriate norming the distribution of this random element in $ C({S^1})$ converges weakly as $ t\, \to \,\infty $. The limit is identified as $ 2(B(x)\, - \,\int {B(y)\,dy)} $ where B is the Brownian bridge. The result is applied to obtain the asymptotic distribution of a Cramer-von Mises type statistic for the global deviation of the local time from the constant t on $ {S^1}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60F05, 60J55

Retrieve articles in all journals with MSC: 60F05, 60J55

Additional Information

PII: S 0002-9947(1979)0536950-9
Keywords: Brownian motion on the circle, local time, weak convergence
Article copyright: © Copyright 1979 American Mathematical Society