Statistical analysis of the first passage path ensemble of jump processes
arXiv:1701.04270 · doi:10.1007/s10955-017-1949-x
Abstract
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.
35 pages
References in corpus (5)
- First-passage times in complex scale-invariant media
- Detecting Memory and Structure in Human Navigation Patterns Using Markov Chain Models of Varying Order
- Steady state and mean recurrence time for random walks on stochastic temporal networks
- Flows in Complex Networks: Theory, Algorithms, and Application to Lennard-Jones Cluster Rearrangement
- Path statistics, memory, and coarse-graining of continuous-time random walks on networks