Asymptotics of the generating function for the volume of the Wiener sausage
type: Item
instance of: scholarly article
title: Asymptotics of the generating function for the volume of the Wiener sausage
zbMATH Open document ID: 0801.60067
DOI: 10.1007/BF01199898
author: Erwin Bolthausen
author: M. van den Berg
publication date: 1994-11-21T00:00:00Z
review text: We consider the generating function \(\mathbb{E} \exp (\lambda | C_ \varepsilon (t) |)\) of the volume of the Wiener sausage \(C_ \varepsilon (t)\), which is the \(\varepsilon\)-neighbourhood of the Wiener path in the time interval \([0,t]\). For \(\lambda < 0\), the limiting behaviour for \(t \to \infty\), up to logarithmic equivalence, had been determined in a celebrated work of Donsker and Varadhan. For \(\lambda > 0\) it had been investigated by the first author and \textit{B. Tóth} [ibid. 88, No. 2, 249-259 (1991; Zbl 0717.60093)], but in contrast to the case \(\lambda < 0\), there is no simple expression for the exponential rate known. We determine the asymptotic behaviour of this rate for small and large \(\lambda\).
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 639365
zbMATH Keywords: generating function
zbMATH Keywords: Wiener sausage
zbMATH Keywords: exponential rate
MaRDI profile type: Publication
cites work: Exponential estimates for the Wiener sausage
cites work: Electrostatic capacity, heat flow, and brownian motion
cites work: Some bounds and limiting results for the measure of Wiener sausage of small radius associated with elliptic diffusions
full work available at URL: https://doi.org/10.1007/bf01199898
OpenAlex ID: W1973986777
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 639365