We present a theory of frequency-dependent counting statistics of electron
transport through nanostructures within the framework of Markovian quantum
master equations. Our method allows the calculation of finite-frequency current
cumulants of arbitrary order, as we explicitly show for the second- and
third-order cumulants. Our formulae generalize previous zero-frequency
expressions in the literature and can be viewed as an extension of MacDonald's
formula beyond shot noise. When combined with an appropriate treatment of
tunneling, using, e.g. Liouvillian perturbation theory in Laplace space, our
method can deal with arbitrary bias voltages and frequencies, as we illustrate
with the paradigmatic example of transport through a single resonant level
model. We discuss various interesting limits, including the recovery of the
fluctuation-dissipation theorem near linear response, as well as some drawbacks
inherent of the Markovian description arising from the neglect of quantum
fluctuations.Comment: Accepted in New Journal of Physics. Updated tex