Approximations of the Wiener sausage and its curvature measures

Details Approximations of the Wiener sausage and its curvature measures Approximations of the Wiener sausage and its curvature measures

2009-10-20

arxiv.org/abs/0910.3841v1

Annals of Applied Probability 2009, Vol. 19, No. 5, 1840-1859

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP596 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

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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