Analytical expressions for mean first passage time for barrier crossing

Question

Consider a particle in a bistable potential. I was wondering if there are analytical expressions for the mean first passage time for crossing the barrier in all three regimes of friction. I am aware that these expressions (Kramers first passage time ) do exist, but they seem to be independent of the initial conditions i.e ( initial position and velocity of the particle in the well ). In other words, I would like an initial position, initial velocity dependent expressions for first passage times in all three regimes of friction i.e ( low friction, moderate to high friction and very high friction). Assume that the energy at barrier is very high as compared to kT. I would be really grateful for any pointers or references in this regard,