  We study nano-pattern formation in a stochastic model for
adsorption-desorption processes with interacting adsorbate and hyperbolic
transport caused by memory effects. It is shown that at early stages the system
manifests pattern selection processes. Stationary stable patterns of nano-size
are analyzed. It was found that multiplicative noise satisfying
fluctuation-dissipation relation can induce re-entrant pattern formation
related to non-equilibrium transitions. According to obtained Fokker-Planck
equation kinetics of island sizes in a quasi-stationary limit is discussed.
Analytical results are compared with computer simulations.
