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October, 1986 Sur La Saucisse De Wiener et les Points Multiples du Mouvement Brownien
Jean-Francois Le Gall
Ann. Probab. 14(4): 1219-1244 (October, 1986). DOI: 10.1214/aop/1176992364


Let $B$ be a Brownian motion with values in Euclidean space $R^d$, where $d = 2 \text{or} 3$. The Wiener sausage with radius $\varepsilon$ associated with $B$ is defined as the set of points whose distance from the path is less than $\varepsilon$. Let $B'$ be another Brownian motion with values in $R^d$, independent of $B$. The Lebesgue measure of the intersection of the Wiener sausages associated with $B$ and $B'$, suitably normalized, is shown to converge, when $\varepsilon$ goes to 0, towards the intersection local time of $B$ and $B'$, as defined by German, Horowitz and Rosen. This approximation of the intersection local time is used to prove a conjecture of Taylor, relating to the Hausdorff measure of the set of multiple points of planar Brownian motion.


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Jean-Francois Le Gall. "Sur La Saucisse De Wiener et les Points Multiples du Mouvement Brownien." Ann. Probab. 14 (4) 1219 - 1244, October, 1986.


Published: October, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0621.60083
MathSciNet: MR866344
Digital Object Identifier: 10.1214/aop/1176992364

Primary: 60J65
Secondary: 60G17 , 60J55

Keywords: Hausdorff measure , Intersection local time , multiple points , Wiener sausage

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 4 • October, 1986
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