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Asymptotics of the generating function for the volume of the Wiener sausage

✍ Scribed by Michiel Berg; Erwin Bolthausen

Publisher
Springer
Year
1994
Tongue
English
Weight
255 KB
Volume
99
Category
Article
ISSN
1432-2064

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We calculate the form of the large time asymptotic expansion of the expected volume of the pinned Wiener sausage associated to a compact set K in R d in dimensions d 3. In each case the leading coefficient is given by the Newtonian capacity of K. If K is a ball of radius a>0 the first three coeffici

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## Abstract We investigate the large time behaviour of the expected volume of the pinned Wiener sausage associated to a compact subset __K__ in \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ {\mathbb R}^d $\end{document} for __d__ β©Ύ 3. The structure of the asymptotic

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## Abstract For parallel neighborhoods of the paths of the __d__ ‐dimensional Brownian motion, so‐called __Wiener sausages__, formulae for the expected surface area are given for any dimension __d__ β‰₯ 2. It is shown by means of geometric arguments that the expected surface area is equal to the firs