  We investigate electrical transport through a single-electron transistor
coupled to a nanomechanical oscillator. Using a combination of a
master-equation approach and a numerical Monte Carlo method, we calculate the
average current and the current noise in the strong-coupling regime, studying
deviations from previously derived analytic results valid in the limit of
weak-coupling. After generalizing the weak-coupling theory to enable the
calculation of higher cumulants of the current, we use our numerical approach
to study how the third cumulant is affected in the strong-coupling regime. In
this case, we find an interesting crossover between a weak-coupling transport
regime where the third cumulant heavily depends on the frequency of the
oscillator to one where it becomes practically independent of this parameter.
Finally, we study the spectrum of the transport noise and show that the two
peaks found in the weak-coupling limit merge on increasing the coupling
strength. Our calculation of the frequency-dependence of the noise also allows
to describe how transport-induced damping of the mechanical oscillations is
affected in the strong-coupling regime.
