# On the volume of the Wiener sausage - Zurich Open Repository and Archive

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

## 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.

## 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.

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Wiener sausage; large deviations English 1990 21 May 2010 08:01 05 Apr 2016 13:29 Institute of Mathematical Statistics 0091-1798 https://doi.org/10.1214/aop/1176990633 http://www.zentralblatt-math.org/zmath/en/search/?q=an:0718.60021

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