On the global asymptotic behavior of Brownian local time on the circle
Author:
E. Bolthausen
Journal:
Trans. Amer. Math. Soc. 253 (1979), 317328
MSC:
Primary 60F05; Secondary 60J55
MathSciNet review:
536950
Fulltext PDF Free Access
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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 . It is shown that after appropriate norming the distribution of this random element in converges weakly as . The limit is identified as where B is the Brownian bridge. The result is applied to obtain the asymptotic distribution of a Cramervon Mises type statistic for the global deviation of the local time from the constant t on .
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 P. Billingsley, Convergence of probability measures, Wiley, New York, 1968. MR 0233396 (38:1718)
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 H. P. McKean, Brownian local times, Topics in Probability Theory, D. W. Stroock and S. R. S. Vardahan (editors), Courant Inst. Math. Sci., New York Univ., New York, 1973, pp. 5992.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197905369509
PII:
S 00029947(1979)05369509
Keywords:
Brownian motion on the circle,
local time,
weak convergence
Article copyright:
© Copyright 1979
American Mathematical Society
