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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The asymptotic behavior of the local time of Brownian motion on the circle is investigated. For fixed time point this is a (random) continuous function on . It is shown that after appropriate norming the distribution of this random element in converges weakly as . The limit is identified as where 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 on .
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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Uncontrolled Keywords:||Brownian motion on the circle; local time; weak convergence|
|Deposited On:||30 Oct 2009 14:58|
|Last Modified:||28 Nov 2013 01:03|
|Publisher:||American Mathematical Society|
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