On the relation between event-based and time-based current statistics

Current statistics can be calculated in various ways. Event-based approaches use the
statistics of the number of events occurring during a given time. Time-based approaches use the
statistics of the time needed to reach a given number of events. By analyzing normal as well as
anomalous statistics of nonequilibrium currents through a two level system in contact with two
different reservoirs, we investigate the conditions under which these different statistics do or do not
yield identical predictions. We rely on the continuous time random walk formulation introduced
in our earlier work (Phys. Rev. E, 77 (2008) 051119).