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Journal Article
On the Volume of the Wiener Sausage
E. Bolthausen
The Annals of Probability
Vol. 18, No. 4 (Oct., 1990), pp. 1576-1582
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2244335
Page Count: 7
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Abstract
Let W(t, ε) be the ε-Wiener sausage, i.e., the ε-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 ε depends on t and converges to 0 with a certain rate.
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The Annals of Probability © 1990 Institute of Mathematical Statistics