  We analyze the transport properties of a semiconductor based bilayer system
under non-equilibrium conditions with special emphasis on the charge transfer
statistics in the regime dominated by the exciton transport. We consider two
different models. In one of them the transport occurs incoherently and is
dominated by incoherent tunneling processes of individual excitons, while in
the other system no disorder is present and transport processes are fully
coherent. We find that the strength of cross correlations of currents in
different layers is only insignificantly affected by the disorder and shows up
similar behaviour in both systems. We discuss possible experimental
realizations and make predictions for measurable quantities.
