  We estimate the time a point or set, respectively, requires to approach the
attractor of a radially symmetric gradient type stochastic differential
equation driven by small noise. Here, both of these times tend to infinity as
the noise gets small. However, the rates at which they go to infinity differ
significantly. In the case of a set approaching the attractor, we use large
deviation techniques to show that this time increases exponentially. In the
case of a point approaching the attractor, we apply a time change and compare
the accelerated process to another process and obtain that this time increases
merely linearly.
