Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 19, Number 5 (2009), 1840-1859.
Approximations of the Wiener sausage and its curvature measures
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.
Ann. Appl. Probab., Volume 19, Number 5 (2009), 1840-1859.
First available in Project Euclid: 16 October 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
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. https://projecteuclid.org/euclid.aoap/1255699545