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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22882

# Bolthausen, E (1990). On the volume of the Wiener sausage. The Annals of Probability, 18(4):1576-1582.

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## Abstract

Let $W(t, \varepsilon)$ be the $\varepsilon$-Wiener sausage, i.e., the $\varepsilon$-neighborhood of the trace of the Brownian motion up to time $t$. It is shown that the results of Donsker and Varadhan on the behavior of $E(\exp(-\nu|W(t, \varepsilon)|)), \nu > 0$, remain true if $\varepsilon$ depends on $t$ and converges to 0 with a certain rate.