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.
"On the expected volume of the Wiener sausage." J. Math. Soc. Japan 62 (4) 1113 - 1136, October, 2010. https://doi.org/10.2969/jmsj/06241113