  We introduce a class of discrete random walk model driven by global memory
effects. At any time the right-left transitions depend on the whole previous
history of the walker, being defined by an urn-like memory mechanism. The
characteristic function is calculated in an exact way, which allows us to
demonstrate that the ensemble of realizations is ballistic. Asymptotically each
realization is equivalent to that of a biased Markovian diffusion process with
transition rates that strongly differs from one trajectory to another. Using
this "inhomogeneous diffusion" feature the ergodic properties of the dynamics
are analytically studied through the time-averaged moments. In the long time
regime they becomes random objects. While their mean values recover the
corresponding ensemble averages, departure between time and ensemble averages
is explicitly shown through their probability densities. For the density of the
second time-averaged moment an ergodic limit and the limit of infinite lag
times do not commutate. All these effects are induced by the memory effects.
