The exact Hausdorff measure of the level sets of Brownian motion |
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Authors: | Edwin Perkins |
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Institution: | (1) Department of Mathematics, University of British Columbia, V6T 1Y4 Vancouver, B.C., Canada |
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Abstract: | Summary We show that if s(t, x) is the local time of a Brownian motion B, and (t)=(2t¦log|logt)1/2 then –m({s=x})=s(t,x) for all t>=0 and x real a.s., where –m(E) is the Hausdorff -measure of E. This solves a problem of Taylor and Wendel who proved the above equality, up to a multiplicative constant, for x=0. |
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