2005/08/26 by Ophir Flomenbom, Joseph Klafter, J. Klafter · 3 citations
Decision Sciences · Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design #cond-mat.other #cond-mat.soft
paper · pdf · doi:10.1103/physrevlett.95.098105
published as Phys. Rev. Lett. 95, 098105 (2005)
openalex publication_date 2005/08/26 · arxiv created 2007/02/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Continuous time random walks (CTRWs) on finite arbitrarily inhomogeneous chains are studied. By introducing a technique of counting all possible trajectories, we derive closed-form solutions in Laplace space for the Green's function (propagator) and for the first passage time probability density function (PDF) for nearest neighbor CTRWs in terms of the input waiting time PDFs. These solutions are also the Laplace space solutions of the generalized master equation. Moreover, based on our counting technique, we introduce the adaptor function for expressing higher order propagators (joint PDFs of time-position variables) for CTRWs in terms of Green's functions. Using the derived formula, an escape problem from a biased chain is considered.