First passage times and asymmetry of DNA translocation

Motivated by experiments in which single-stranded DNA with a short hairpin loop at one end undergoes unforced diffusion through a narrow pore, we study the first passage times for a particle, executing one-dimensional Brownian motion in an asymmetric sawtooth potential, to exit one of the boundaries. We consider the first passage times for the case of classical diffusion, characterized by a mean-square displacement of the form <(Delta(x))2> approximately t, and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form <(Delta(x))2> approximately t(gamma) with 0