Exit times in non-Markovian drifting continuous-time random walk processes

Details Exit times in non-Markovian drifting continuous-time random walk processes Exit times in non-Markovian drifting continuous-time random walk processes

2010-02-02

arxiv.org/abs/1002.0571v2

Phys. Rev. 82, 021102 (2010)

Mathematics

Probability

9 pages, 3 color plots, two-column revtex 4; new Appendix and references added

Scientific paper

10.1103/PhysRevE.82.021102

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.

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