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

Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-23138

Bolthausen, E (1979). On the global asymptotic behavior of Brownian local time on the circle. Transactions of the American Mathematical Society, 253:317-328.

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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 $t \rightarrow \infty$ . 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 $S^1$ .

Item Type:	Journal Article, refereed, original work
Communities & Collections:	07 Faculty of Science > Institute of Mathematics
DDC:	510 Mathematics
Uncontrolled Keywords:	Brownian motion on the circle; local time; weak convergence
Language:	English
Date:	1979
Deposited On:	30 Oct 2009 15:58
Last Modified:	23 Nov 2012 13:36
Publisher:	American Mathematical Society
ISSN:	0002-9947
Publisher DOI:	10.2307/1998200
Related URLs:	http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0413.60012
WoS Citation Count:	3

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