  A theoretical approach for the non-equilibrium transport properties of
nanoscale systems coupled to metallic electrodes with strong electron-phonon
interactions is presented. It consists in a resummation of the dominant Feynman
diagrams from the perturbative expansion in the coupling to the leads. We show
that this scheme eliminates the main pathologies found in previous simple
analytical approaches for the polaronic regime. The results for the spectral
and transport properties are compared with those from several other approaches
for a wide range of parameters. The method can be formulated in a simple way to
obtain the full counting statistics. Results for the shot and thermal noise are
presented.
