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

Abstract

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.

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

References in corpus (4)

• The continuous time random walk formalism in financial markets
• On the effect of random inhomogeneities in Kerr-media modelled by non-linear Schrodinger equation
• Crossover between Levy and Gaussian regimes in first passage processes
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Cited by in corpus (1)

• Monotonous continuous-time random walks with drift and stochastic reset events