2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126717We generalize the stochastic path integral formalism by considering Hamiltonian dynamics in the presence of general Markovian noise. Kramers' solution of the activation rate for escape over a barrier is generalized for non-Gaussian driving noise in both the overdamped and underdamped limit. We apply our general results to a Josephson junction detector measuring the electron counting statistics of a mesoscopic conductor. Activation rate dependence on the third current cumulant includes an additional term originating from the back-action of the measurement circuit.5 pages, 2 figures, discussion of experiment added, typos correctedMesoscale and Nanoscale PhysicsStatistical Mechanicstext