Escapes And Transitions In Overdamped Systems On Short Times: General Solution

We find the complete general solution of the noise-induced escape/transition problem on time scales less than or order of the relaxation time. The theory is checked in simulations. The most interesting unsolved problems are: (i) calculation of the first-order correction and matching of our results with those by Shneidman obtained for larger time-scales by a different method; (ii) generalization to transitions in a bistable potential driven by a moderately slow and strong periodic force, which may be relevant for bilogical applications.