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August, 1985 Brownian Paths and Cones
Krzysztof Burdzy
Ann. Probab. 13(3): 1006-1010 (August, 1985). DOI: 10.1214/aop/1176992922


If $\cos(\theta/2) < 1/\sqrt n$ then a.s. there are times $0 \leq s_1 < s_2$ such that the $n$-dimensional Brownian motion $Z(t)$ stays for all $t \in (s_1, s_2)$ in a cone with vertex $Z(s_1)$ and angle $\theta$. If $\cos(\theta/2) > 1/\sqrt n$ then the same event has probability 0.


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Krzysztof Burdzy. "Brownian Paths and Cones." Ann. Probab. 13 (3) 1006 - 1010, August, 1985.


Published: August, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0574.60053
MathSciNet: MR799436
Digital Object Identifier: 10.1214/aop/1176992922

Primary: 60J65
Secondary: 60G17

Keywords: Brownian motion , Brownian paths , local properties of trajectories

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 3 • August, 1985
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