Time and Palm stationarity of repairable systems

In this paper we study asymptotic behaviour of marked point processes describing failure processes of repairable systems in which repair decisions depend on the past. Under natural conditions on system parameters such processes admit unique time stationary distributions and are ergodic. Convergence of moments and mean number of failures as well as central limit theorems will be established. The methods used in this paper combine classical Palm-martingale calculus for marked point processes with stability results for Harris recurrent Markov processes.