  We present an experimental investigation of stochastic switching of a
bistable Josephson junctions array resonator with a resonance frequency in the
GHz range. As the device is in the regime where the anharmonicity is on the
order of the linewidth, the bistability appears for a pump strength of only a
few photons. We measure the dynamics of the bistability by continuously
observing the jumps between the two metastable states, which occur with a rate
ranging from a few Hz down to a few mHz. The switching rate strongly depends on
the pump strength, readout strength and the temperature, following Kramer's
law. The interplay between nonlinearity and coupling, in this little explored
regime, could provide a new resource for nondemolition measurements, single
photon switches or even elements for autonomous quantum error correction.
