  We analyze the tail behavior of the maximum N of Brownian motion minus a
parabola and give an asymptotic expansion for P(N>x) as x tends to infinity.
This extends a first order result on the tail behavior, which can be deduced
from Huesler and Piterbarg (1999). We also point out the relation between
certain results in Groeneboom (2010) and Janson, Louchard and Martin-L\"of
(2010).
