The escape rate from a point attractor across an unstable fixed point
is studied for a noisy map dynamics in 1 dimension. It is shown that f
or additive white noise xi with a distribution proportional to exp[-\x
i\(alpha)], alpha > 1, the escape rate is dominated by an exponentiall
y leading Arrhenius-like factor in the weak-noise limit. However, with
the exception of Gaussian noise (alpha = 2), the pre-exponential cont
ribution to the rate still depends more strongly than any power law on
the noise strength.