  The slow drift (with speed $\eps$) of a parameter through a pitchfork
bifurcation point, known as the dynamic pitchfork bifurcation, is characterized
by a significant delay of the transition from the unstable to the stable state.
We describe the effect of an additive noise, of intensity $\sigma$, by giving
precise estimates on the behaviour of the individual paths. We show that until
time $\sqrt\eps$ after the bifurcation, the paths are concentrated in a region
of size $\sigma/\eps^{1/4}$ around the bifurcating equilibrium. With high
probability, they leave a neighbourhood of this equilibrium during a time
interval $[\sqrt\eps, c\sqrt{\eps\abs{\log\sigma}}]$, after which they are
likely to stay close to the corresponding deterministic solution. We derive
exponentially small upper bounds for the probability of the sets of exceptional
paths, with explicit values for the exponents.
