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Time and Palm stationarity of repairable systems

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  • Last, Günter
  • Szekli, Ryszard

Abstract

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.

Suggested Citation

  • Last, Günter & Szekli, Ryszard, 1999. "Time and Palm stationarity of repairable systems," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 17-43, January.
    • Handle: RePEc:eee:spapps:v:79:y:1999:i:1:p:17-43
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    References listed on IDEAS

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    1. Lindvall, Torgny, 1988. "Ergodicity and inequalities in a class of point processes," Stochastic Processes and their Applications, Elsevier, vol. 30(1), pages 121-131, November.
    2. Last, Günter, 1996. "Coupling with compensators," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 147-170, December.
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    2. Last, Günter, 1996. "Coupling with compensators," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 147-170, December.

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