  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 non-stochastic and non-iterative 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.
