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

Michiel van den Berg, Erwin Bolthausen

Research output: Contribution to journalArticle

Abstract

We consider the generating function {Mathematical expression} of the voltime of the Wiener sausage C?(t), which is the e-neighbourhood of the Wiener path in the time interval [0, t]. For ?<0, the limiting behavior for t?8, up to logarithmic equivalence, had been determined in a celebrated work of Donsker and Varadhan. For ?>0 it had been investigated by van den Berg and Tóth, but in contrast to the case ?<0, there is no simple expression for the exponential rate known. We determine the asymptotic behaviour of this rate for small and large ?. © 1984 Springer-Verlag.

Original languageEnglish
Pages (from-to)389-397
Number of pages9
JournalProbability Theory and Related Fields
Volume99
Issue number3
DOIs
Publication statusPublished - Sep 1994

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Wiener Sausage
Generating Function
Limiting Behavior
Logarithmic
Asymptotic Behavior
Equivalence
Path
Interval

Keywords

  • Mathematics Subject Classification (1994): 60J65, 60F10, 60J45

Cite this

van den Berg, Michiel ; Bolthausen, Erwin. / Asymptotics of the generating function for the volume of the Wiener sausage. In: Probability Theory and Related Fields. 1994 ; Vol. 99, No. 3. pp. 389-397.
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Asymptotics of the generating function for the volume of the Wiener sausage. / van den Berg, Michiel; Bolthausen, Erwin.

In: Probability Theory and Related Fields, Vol. 99, No. 3, 09.1994, p. 389-397.

Research output: Contribution to journalArticle

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