Moments of the First Passage Time under External Driving

摘要: A general theory is derived for the moments of first passage time a one-dimensional Markov process in presence weak time-dependent forcing. The linear corrections to can be expressed by quadratures potential and probability density unperturbed system or equivalently its Laplace transform. If none latter functions known, formulas may still useful specific cases including slow driving with power at only small large times. In second part paper, explicit expressions mean variance are parabolic an exponentially decaying force. analytical results found excellent agreement computer simulations respective first-passage processes. particular examples furthermore demonstrate that already effect simple exponential fairly involved implying nontrivial nonmonotonic behavior as driving’s scale.