Transient Fluctuations in the Decay of an Unstable State

The decay of an unstable state by the stochastic time of intersection of a given threshold is described. This stochastic parameter is characterized by closed moment equations exactly soluble, whereas previous approaches, in terms of stochastic amplitudes sampled at a fixed time, led to an open hierarchy of equations requiring approximate solutions. The relevance of this new description is shown by the fit with the experimental transient fluctuations of an unstable system.