Exit times in non-Markovian drifting continuous-time random walk processes
arXiv:1002.0571 · doi:10.1103/PhysRevE.82.021102
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 (13)
- Diffusion of Earthquake Aftershock Epicenters, Omori's Law and Generalized Continuous-Time Random Walk Models
- Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation
- A continuous time random walk model for financial distributions
- Power-Law Time Distribution of Large Earthquakes
- Anomalous diffusion and the first passage time problem
- Stochastic calculus for uncoupled continuous-time random walks
- The continuous time random walk formalism in financial markets
- Long-Tailed Trapping Times and Levy Flights in a Self-Organized Critical Granular System
- Scaling and data collapse for the mean exit time of asset prices
- Extreme times 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
- On properties of Continuous-Time Random Walks with Non-Poissonian jump-times