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.
Publié le : 2010-10-15
Classification:
Wiener sausage,
power series,
Laplace transform,
Bessel process,
60J65,
60D05,
44A10,
30B10
@article{1288703099,
author = {HAMANA, Yuji},
title = {On the expected volume of the Wiener sausage},
journal = {J. Math. Soc. Japan},
volume = {62},
number = {1},
year = {2010},
pages = { 1113-1136},
language = {en},
url = {http://dml.mathdoc.fr/item/1288703099}
}
HAMANA, Yuji. On the expected volume of the Wiener sausage. J. Math. Soc. Japan, Tome 62 (2010) no. 1, pp. 1113-1136. http://gdmltest.u-ga.fr/item/1288703099/