Repository: Freie Universität Berlin, Math Department

Statistical Analysis of the First Passage Path Ensemble of Jump Processes

von Kleist, M. and Schütte, Ch. and Zhang, W. (2018) Statistical Analysis of the First Passage Path Ensemble of Jump Processes. Journal of Statistical Physics, 170 (4). pp. 809-843.

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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.

Item Type:Article
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:2240
Deposited By: BioComp Admin
Deposited On:26 Feb 2018 11:06
Last Modified:26 Feb 2018 11:06

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