Minimal dimension linear filters for stationary Markov processes with finite state space

1991 ◽  
Vol 36 (1) ◽  
pp. 1-19 ◽  
Author(s):  
G. B. Di Masi ◽  
P. Kitsul ◽  
R. S. Liptser
Keyword(s):  
State Space ◽  
Markov Processes ◽  
Linear Filters ◽  
Minimal Dimension ◽  
Finite State ◽  
Finite State Space

Monotone Markov processes with respect to the reversed hazard rate ordering: an application to reliability

2001 ◽  
Vol 38 (1) ◽  
pp. 195-208 ◽  
Author(s):  
Sophie Bloch-Mercier
Keyword(s):  
Markov Process ◽  
State Space ◽  
Markov Processes ◽  
Hazard Rate ◽  
Repairable System ◽  
Reversed Hazard Rate ◽  
Up States ◽  
Finite State ◽  
Hazard Rate Ordering ◽  
Finite State Space

We consider a repairable system with a finite state space which evolves in time according to a Markov process as long as it is working. We assume that this system is getting worse and worse while running: if the up-states are ranked according to their degree of increasing degradation, this is expressed by the fact that the Markov process is assumed to be monotone with respect to the reversed hazard rate and to have an upper triangular generator. We study this kind of process and apply the results to derive some properties of the stationary availability of the system. Namely, we show that, if the duration of the repair is independent of its completeness degree, then the more complete the repair, the higher the stationary availability, where the completeness degree of the repair is measured with the reversed hazard rate ordering.

Monotone Markov processes with respect to the reversed hazard rate ordering: an application to reliability

2001 ◽  
Vol 38 (01) ◽  
pp. 195-208 ◽  
Author(s):  
Sophie Bloch-Mercier
Keyword(s):  
Markov Process ◽  
State Space ◽  
Markov Processes ◽  
Hazard Rate ◽  
Repairable System ◽  
Reversed Hazard Rate ◽  
Up States ◽  
Finite State ◽  
Hazard Rate Ordering ◽  
Finite State Space

We consider a repairable system with a finite state space which evolves in time according to a Markov process as long as it is working. We assume that this system is getting worse and worse while running: if the up-states are ranked according to their degree of increasing degradation, this is expressed by the fact that the Markov process is assumed to be monotone with respect to the reversed hazard rate and to have an upper triangular generator. We study this kind of process and apply the results to derive some properties of the stationary availability of the system. Namely, we show that, if the duration of the repair is independent of its completeness degree, then the more complete the repair, the higher the stationary availability, where the completeness degree of the repair is measured with the reversed hazard rate ordering.

Rate modulation in dams and ruin problems

1996 ◽  
Vol 33 (2) ◽  
pp. 523-535 ◽  
Author(s):  
Søren Asmussen ◽  
Offer Kella
Keyword(s):  
State Space ◽  
Release Rate ◽  
Risk Process ◽  
The State ◽  
Limiting Distribution ◽  
Process Conditions ◽  
Explicit Formulas ◽  
Rate Modulation ◽  
Finite State ◽  
Finite State Space

We consider a dam in which the release rate depends both on the state and some modulating process. Conditions for the existence of a limiting distribution are established in terms of an associated risk process. The case where the release rate is a product of the state and the modulating process is given special attention, and in particular explicit formulas are obtained for a finite state space Markov modulation.

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