On the global asymptotic behavior of Brownian local time on the circle
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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 $t \to \infty$. 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
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 253 (1979), 317-328
- MSC: Primary 60F05; Secondary 60J55
- DOI: https://doi.org/10.1090/S0002-9947-1979-0536950-9
- MathSciNet review: 536950