Annals of Applied Probability

Approximations of the Wiener sausage and its curvature measures

Jan Rataj, Evgeny Spodarev, and Daniel Meschenmoser

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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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Ann. Appl. Probab., Volume 19, Number 5 (2009), 1840-1859.

First available in Project Euclid: 16 October 2009

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Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

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


Rataj, Jan; Spodarev, Evgeny; Meschenmoser, Daniel. Approximations of the Wiener sausage and its curvature measures. Ann. Appl. Probab. 19 (2009), no. 5, 1840--1859. doi:10.1214/09-AAP596.

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