Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 62, Number 4 (2010), 1113-1136.
On the expected volume of the Wiener sausage
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 t1/2 as t tends to 0 and that it is represented as an absolutely convergent power series of t1/2 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.
J. Math. Soc. Japan, Volume 62, Number 4 (2010), 1113-1136.
First available in Project Euclid: 2 November 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 44A10: Laplace transform 30B10: Power series (including lacunary series)
HAMANA, Yuji. On the expected volume of the Wiener sausage. J. Math. Soc. Japan 62 (2010), no. 4, 1113--1136. doi:10.2969/jmsj/06241113. https://projecteuclid.org/euclid.jmsj/1288703099