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October 2009 Approximations of the Wiener sausage and its curvature measures
Jan Rataj, Evgeny Spodarev, Daniel Meschenmoser
Ann. Appl. Probab. 19(5): 1840-1859 (October 2009). DOI: 10.1214/09-AAP596


A parallel neighborhood of a path of a Brownian motion is sometimes called the Wiener sausage. We consider almost sure approximations of this random set by a sequence of random polyconvex sets and show that the convergence of the corresponding mean curvature measures holds under certain conditions in two and three dimensions. Based on these convergence results, the mean curvature measures of the Wiener sausage are calculated numerically by Monte Carlo simulations in two dimensions. The corresponding approximation formulae are given.


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Jan Rataj. Evgeny Spodarev. Daniel Meschenmoser. "Approximations of the Wiener sausage and its curvature measures." Ann. Appl. Probab. 19 (5) 1840 - 1859, October 2009.


Published: October 2009
First available in Project Euclid: 16 October 2009

zbMATH: 1205.60146
MathSciNet: MR2569809
Digital Object Identifier: 10.1214/09-AAP596

Primary: 60J65
Secondary: 60D05

Keywords: Brownian motion , Euler–Poincaré characteristic , intrinsic volumes , mean curvature measures , Minkowski functionals , parallel neighborhood , polyconvex approximation , tube , Wiener sausage

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.19 • No. 5 • October 2009
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