Passage times for the decay of a time-dependent unstable state

We study the decay of an unstable state when the control parameter is sweeping as a(t)=-${\mathit{a}}_0$+${\mathit{bt}}^{\mathrm{\delta }}$. We introduce an approximation for the cumulative distribution. This allows, in the limit of small noise, the calculation of the first-passage-time distribution and the moment generating function analytically. The transient moments and anomalous fluctuation for the full nonlinear process are calculated using stochastic instantonlike trajectories centered on the first-passage time.