We consider the combined effect of shot and thermal noise on (i) the stationary distribution of fluctuations about the nonzero voltage state of an underdamped hysteretic Josephson junction, and (ii) the noise induced transition rate from the nonzero voltage to the zero voltage state. We find that the distribution is nonsymmetric in that the positive voltage fluctuations are more probable than the negative ones. We also find that the transition rates are larger than those due to thermal noise alone.