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  Time and Palm stationarity of repairable systems Gunter Last 1

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by Ryszard Szekli
http://www.mathematik.tu-bs.de/preprints/199717.ps
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Abstract:

Abstract: In this paper we study the asymptotic behaviour of a marked point process describing the failure process of a repairable system in which repairs depend on the history of the process. Under natural conditions on the system parameters the process admits a unique time stationary distribution and satisfies ergodicity results. Convergences of moments and mean number of failures as well as central limit theorems for the Palm stationary version of the process will be discussed. The methods used in this paper combine Palm--martingale calculus for marked point processes with recent stability results for Harris recurrent Markov processes.

Citations

159 Lectures on the Coupling Method – Lindvall - 2002
32 Stability of Markovian processes III: Foster-Lyapunov criteria for continuous time processes – Meyn, Tweedie - 1993
21 Multivariate Point Processes: Predictable Projection, RadonNikodym Derivatives, Representation of Martingales – Jacod - 1975
9 Mixing properties of Harris chains and autoregressive processes – Athreya, Pantula - 1986
8 Age-dependent minimal repair – Block, Borges, et al. - 1985
6 Imbedded construction of stationary sequences and point processes with a random memory, Queueing Systems 17 – Br'emaud, Massouli'e - 1994
6 Some results for repairable systems – Kijima - 1989
4 Exponential ergodicity of Markov processes, Annals of Probability 23 – Down, Meyn, et al. - 1995
2 Repairable Systems Reliability, Lecture Notes in Statistics, vol. 7 – Ascher, Feingold - 1984
2 Coupling with compensators, Stochastic Process – Last - 1996
1 Piecewise-deterministic Markov processes: A general class of non-diffusion stochastic models – Davies - 1984
1 Report no 87, University of Wroclaw, submitted for publication (1997a – Last, Szekli - 1988
1 Tweedie R.L., Stability of Markovian Processes I: Criteria for descrete time chains – P, L - 1992
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