Topics: Markov Chain - Stochastic Process
(definition)
In the context of a Markov chain, the first-passage time is the minimum amount of transitions that are necessary to go from one state to another for the first time.
Compare to the recurrence time, which is the minimum amount of steps needed to return to a given state (for the first time, too).
We can obtain the average first-passage time for a given state when starting at another given state.