Minimal dimensional linear filters for discrete-time Markov processes with finite state space

1996 ◽  
Vol 41 (10) ◽  
pp. 1545-1549 ◽  
Author(s):  
G.B. Di Masi ◽  
P.I. Kitsul
Keyword(s):  
State Space ◽  
Markov Processes ◽  
Discrete Time ◽  
Linear Filters ◽  
Finite State ◽  
Finite State Space

A discrete-time storage process with a general release rule

1989 ◽  
Vol 26 (03) ◽  
pp. 566-583
Author(s):  
John E. Glynn
Keyword(s):  
State Space ◽  
Discrete Time ◽  
Storage System ◽  
Simple Condition ◽  
Storage Process ◽  
Finite State ◽  
Stationary Behaviour ◽  
Finite State Space

A discrete-time storage system with a general release rule and stationary nonnegative inflows is examined. A simple condition is found for the existence of a stationary storage and outflow for a general possibly non-monotone release function. It is also shown that in the Markov case (i.e. independent inflows) these distributions are unique under certain conditions. It is demonstrated that under these conditions the stationary behaviour in the Markov case varies continuously with parametric changes in the release rule. This result is used to prove convergence of a finite state space approximation for the Markov storage system.

A discrete-time storage process with a general release rule

1989 ◽  
Vol 26 (3) ◽  
pp. 566-583 ◽  
Author(s):  
John E. Glynn
Keyword(s):  
State Space ◽  
Discrete Time ◽  
Storage System ◽  
Simple Condition ◽  
Storage Process ◽  
Finite State ◽  
Stationary Behaviour ◽  
Finite State Space

A discrete-time storage system with a general release rule and stationary nonnegative inflows is examined. A simple condition is found for the existence of a stationary storage and outflow for a general possibly non-monotone release function. It is also shown that in the Markov case (i.e. independent inflows) these distributions are unique under certain conditions. It is demonstrated that under these conditions the stationary behaviour in the Markov case varies continuously with parametric changes in the release rule. This result is used to prove convergence of a finite state space approximation for the Markov storage system.

scholarly journals Sojourn times in finite Markov processes

1989 ◽  
Vol 26 (4) ◽  
pp. 744-756 ◽  
Author(s):  
Gerardo Rubino ◽  
Bruno Sericola
Keyword(s):  
Markov Process ◽  
Asymptotic Behaviour ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Sojourn Time ◽  
Sojourn Times ◽  
Finite State ◽  
Sojourn Time Distributions ◽  
Finite State Space

Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the nth sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases. We consider the usually pseudo-aggregated Markov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions in the original Markov process and the moments of the corresponding holding times of the pseudo-aggregated one is also studied.

scholarly journals Sojourn times in finite Markov processes

1989 ◽  
Vol 26 (04) ◽  
pp. 744-756 ◽  
Author(s):  
Gerardo Rubino ◽  
Bruno Sericola
Keyword(s):  
Markov Process ◽  
Asymptotic Behaviour ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Sojourn Time ◽  
Sojourn Times ◽  
Finite State ◽  
Sojourn Time Distributions ◽  
Finite State Space

Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the nth sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases. We consider the usually pseudo-aggregated Markov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions in the original Markov process and the moments of the corresponding holding times of the pseudo-aggregated one is also studied.

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.

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