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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.

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Uncontrolled Keywords:generating function, Wiener sausage, exponential rate
Language:English
Date:1994
Deposited On:20 May 2010 15:13
Last Modified:03 Nov 2024 02:37
Publisher:Springer
ISSN:0178-8051
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/BF01199898
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