  We present a stochastic formulation of the Keldysh theory to calculate the
conductance of a finite Kitaev chain coupled to two electron reservoirs. We
study the dependence of the conductance on the number of sites in the chain and
find that only for sufficiently long chains and in the regime that the chain is
a topological superconducter the conductance at both ends tends to the
universal value $2e^2/h$, as expected on the basis of the contact resistance of
a single conducting channel provided by the Majorana zero mode. In this
topologically nontrivial case we find an exponential decay of the current
inside the chain and a simple analytical expression for the decay length.
Finally, we also study the differential conductance at nonzero bias and the
full current-voltage curves. We find a nonmonotonic behavior of the maximal
current through the Kitaev chain as a function of the coupling strength with
the reservoirs.
