74 research outputs found
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.Comment: Published in at http://dx.doi.org/10.1214/09-AAP596 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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