  Fluctuations in stochastic systems are usually characterized by the full
counting statistics, which analyzes the distribution of the number of events
taking place in the fixed time interval. In an alternative approach, the
distribution of the first-passage times, i.e. the time delays after which the
counting variable reaches a certain threshold value, is studied. This paper
presents the approach to calculate the first-passage time distribution in
systems in which the analyzed current is associated with an arbitrary set of
transitions within the Markovian network. Using this approach it is shown that
when the subsequent first-passage times are uncorrelated there exist strict
relations between the cumulants of the full counting statistics and the
first-passage time distribution. On the other hand, when the correlations of
the first-passage times are present, their distribution may provide additional
information about the internal dynamics of the system in comparison to the full
counting statistics; for example, it may reveal the switching between different
dynamical states of the system. Additionally, I show that breaking of the
fluctuation theorem for first-passage times may reveal the multicyclic nature
of the Markovian network.
