Header

UZH-Logo

Maintenance Infos

Asymptotics of the generating function for the volume of the Wiener sausage


van den Berg, M; Bolthausen, E (1994). Asymptotics of the generating function for the volume of the Wiener sausage. Probability Theory and Related Fields, 99(3):389-397.

Abstract

We consider the generating function exp(λ|C ε (t)|) of the volume of the Wiener sausage C ε (t), which is the ε-neighbourhood of the Wiener path in the time interval [0,t]. For λ<0, the limiting behaviour for t→∞, up to logarithmic equivalence, had been determined in a celebrated work of Donsker and Varadhan. For λ>0 it had been investigated by the first author and B. Tóth, but in contrast to the case λ<0, there is no simple expression for the exponential rate known. We determine the asymptotic behaviour of this rate for small and large λ.

Abstract

We consider the generating function exp(λ|C ε (t)|) of the volume of the Wiener sausage C ε (t), which is the ε-neighbourhood of the Wiener path in the time interval [0,t]. For λ<0, the limiting behaviour for t→∞, up to logarithmic equivalence, had been determined in a celebrated work of Donsker and Varadhan. For λ>0 it had been investigated by the first author and B. Tóth, but in contrast to the case λ<0, there is no simple expression for the exponential rate known. We determine the asymptotic behaviour of this rate for small and large λ.

Statistics

Citations

7 citations in Web of Science®
7 citations in Scopus®
Google Scholar™

Altmetrics

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:generating function; Wiener sausage; exponential rate
Language:English
Date:1994
Deposited On:20 May 2010 15:13
Last Modified:05 Apr 2016 13:28
Publisher:Springer
ISSN:0178-8051
Publisher DOI:https://doi.org/10.1007/BF01199898

Download

Full text not available from this repository.
View at publisher