Bolthausen, E (1990). On the volume of the Wiener sausage. The Annals of Probability, 18(4):1576-1582.
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.
| 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: | 24 Sep 2019 16:19 |
| Publisher: | Institute of Mathematical Statistics |
| ISSN: | 0091-1798 |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1214/aop/1176990633 |
| Related URLs: | http://www.zentralblatt-math.org/zmath/en/search/?q=an:0718.60021 |
Bolthausen, E