title: Graph transformation method for calculating waiting times in Markov chains.
abstract: We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then calculate averages over a given ensemble of paths for both additive and multiplicative properties in a nonstochastic and noniterative fashion. In particular, we can calculate the mean first-passage time between arbitrary groups of stationary points for discrete path sampling databases, and hence extract phenomenological rate constants. We present a number of examples to demonstrate the efficiency and robustness of this approach.
authors.affiliation: University Chemical Laboratories, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom. sat39@cam.ac.uk
authors.forename: Semen A
authors.initials: SA
authors.lastname: Trygubenko
authors.forename: David J
authors.initials: DJ
authors.lastname: Wales