Non-Markovian rotating unstable processes driven by Gaussian colored noise

In this paper the statistical properties of the mean passage time distribution are used to characterize the decay process of non-Markovian rotating unstable processes driven by Gaussian colored noise and subjected to the influence of a constant external force. The time characterization will be linear and studied in two limiting cases: large and intermediate times. General systems of two variables are studied. In both schemes we show that, for small correlation time of the noise, the non-Markovian effects are taken into account by an effective noise intensity. To compare qualitatively the non-Markovian time scale with respect to the Markovian case, we apply those results to determine the detection bandwidth of a large external signal in a laser system.