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Hamana, Yuji

On the expected volume of the Wiener sausage. (English) Zbl 1223.60066

J. Math. Soc. Japan 62, No. 4, 1113-1136 (2010).
Author’s abstract: “We consider the expected volume of the Wiener sausage on the time interval \([0,t]\) associated with a closed ball. Let \(L(t)\) be the expected volume minus the volume of the ball. We obtain that \(L(t)\) is asymptotically equal to a constant multiple of \(t^{1/2}\) as \(t\) tends to 0 and that it is represented as an absolutely convergent power series of \(t^{1/2}\) for any \(t > 0\) in the odd dimensional cases. Moreover, the explicit form of \(L(t)\) can be given in five and seven dimensional cases.”
Reviewer: Ion C. Vladimirescu (Craiova)

Cited in 5 Documents

MSC:

60J65 Brownian motion
60D05 Geometric probability and stochastic geometry
30B10 Power series (including lacunary series) in one complex variable

Keywords:

Wiener sausage; Laplace transform; Bessel process
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\textit{Y. Hamana}, J. Math. Soc. Japan 62, No. 4, 1113--1136 (2010; Zbl 1223.60066)
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