Thermal noise effects on the microwave-induced steps of a current-driven Josephson junction

We study the effects of thermal noise on the microwave-induced steps of a current-driven Josephson junction using the resistively shunted junction model for the junction. We generalize Stephen's method for calculating the width of the steps to the case of an underdamped junction, and to the case of a subharmonic step, provided that there is no overlapping of different steps. In order to treat the case of overlapping steps we introduce a new approach which enables us to calculate the distribution of fluctuations about as well as the transition rates out of the steps. All our results are usually in the form of explicit analytical expressions that facilitate a comparison with experiments