| Summary: | A non-Markovian process, in which stochastic evolution of the system depends on its past history, often shows up in soft matter, living cells, and other complex systems. Despite its importance, however, the statistics of first passage time in such systems is not well understood. This is largely due to the fact that most theoretical frameworks are based on Markovian description, and incorporation of the memory effect into the problem remains a challenge. Here, we argue that a key quantity in the problem, i.e., the average behavior of a non-Markovian walker after the first passage, can be linked to its dynamical response, and propose a simple framework to compute important observables in the first passage problem. We perform a mean-field analysis and demonstrate semiquantitative description of the one-dimensional fractional Brownian motion in the presence of an absorbing boundary.
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