Closed-form solutions for continuous time random walks on finite chains.
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.
Flomenbom
Ophir
O
School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel.
Klafter
Joseph
J
D012321:DNA-Directed RNA Polymerases / Q000378:metabolism; D008390:Markov Chains; D008954:Models, Biological; D008962:Models, Theoretical; D013269:Stochastic Processes
D012321:DNA-Directed RNA Polymerases