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On the volume of the Wiener sausage


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.

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Wiener sausage; large deviations
Language:English
Date:1990
Deposited On:21 May 2010 08:01
Last Modified:05 Apr 2016 13:29
Publisher:Institute of Mathematical Statistics
ISSN:0091-1798
Publisher DOI:10.1214/aop/1176990633
Related URLs:http://www.zentralblatt-math.org/zmath/en/search/?q=an:0718.60021
Permanent URL: http://doi.org/10.5167/uzh-22882

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