  We study thermal instability and formation of local hot spots in a driven
nonlinear NbN superconducting microwave resonator. White noise injected into
the resonator results in transitions between the metastable states via a
process consisting of two stages. In the first stage, the input noise entering
the system induces fluctuations in the resonator mode. While, in the second
one, these mode fluctuations result in phase transitions of the hot spot due to
induced temperature fluctuations. The associated noise-activated escape rate is
calculated theoretically, and also measured experimentally by means of driving
the system into stochastic resonance. A comparison between theory and
experiment yields a partial agreement.
