  The intrinsic nonlinearity of Josephson junctions converts Gaussian current
noise in the input into non-Gaussian voltage noise in the output. For a
resistively shunted Josephson junction with white input noise we determine
numerically exactly the properties of the few lowest cumulants of the voltage
fluctuations, and we derive analytical expressions for these cumulants in
several important limits. The statistics of the voltage fluctuations is found
to be Gaussian at bias currents well above the Josephson critical current, but
Poissonian at currents below the critical value. In the transition region close
to the critical current the higher-order cumulants oscillate and the voltage
noise is strongly non-Gaussian. For coloured input noise we determine the third
cumulant of the voltage.
