## The Annals of Probability

### On the Volume of the Wiener Sausage

E. Bolthausen

#### 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.

#### Article information

Source
Ann. Probab., Volume 18, Number 4 (1990), 1576-1582.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176990633

Digital Object Identifier
doi:10.1214/aop/1176990633

Mathematical Reviews number (MathSciNet)
MR1071810

Zentralblatt MATH identifier
0718.60021

JSTOR