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The very notion of a current fluctuation is problematic in the quantumcontext. We study that problem in the context of nonequilibrium statisticalmechanics, both in a microscopic setup and in a Markovian model. Our answer isbased on a rigorous result that relates the weak coupling limit of fluctuationsof reservoir observables under a global unitary evolution with the statisticsof the so-called quantum trajectories. These quantum trajectories arefrequently considered in the context of quantum optics, but they remain usefulfor more general nonequilibrium systems.  In contrast with the approaches found in the literature, we do not assumethat the system is continuously monitored. Instead, our starting point is arelatively realistic unitary dynamics of the full system.Comment: 18 pages, v1-->v2, Replaced the former Appendix B by a (thematically)  different one. Mainly changes in the introductory Section 2+ added reference

Fluctuations of Quantum Currents and Unravelings of Master Equations