On semi-Markov processes on arbitrary spaces

1969 ◽  
Vol 66 (2) ◽  
pp. 381-392 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Markov Processes ◽  
Borel Sets ◽  
Image Position ◽  
Semi Markov Processes

Let E be an arbitrary set, a σ-algebra of subsets of the Borel sets of F. We write A × B for the product of the sets A and B, andfor the product σ-algebra of and (i.e. the σ-algebra generated by the rectangles A × B with A ∈ and B ∈ ).

Quasi-stationary distributions in semi-Markov processes

1970 ◽  
Vol 7 (02) ◽  
pp. 388-399 ◽  
Author(s):  
C. K. Cheong
Keyword(s):  
Markov Process ◽  
State Space ◽  
Markov Processes ◽  
Transition Probability ◽  
Main Concern ◽  
Initial State ◽  
Stationary Distributions ◽  
Semi Markov Process ◽  
Image Position ◽  
Semi Markov Processes

Our main concern in this paper is the convergence, as t → ∞, of the quantities i, j ∈ E; where Pij (t) is the transition probability of a semi-Markov process whose state space E is irreducible but not closed (i.e., escape from E is possible), and rj is the probability of eventual escape from E conditional on the initial state being i. The theorems proved here generalize some results of Seneta and Vere-Jones ([8] and [11]) for Markov processes.

Quasi-stationary distributions in semi-Markov processes

1970 ◽  
Vol 7 (2) ◽  
pp. 388-399 ◽  
Author(s):  
C. K. Cheong
Keyword(s):  
Markov Process ◽  
State Space ◽  
Markov Processes ◽  
Transition Probability ◽  
Main Concern ◽  
Initial State ◽  
Stationary Distributions ◽  
Semi Markov Process ◽  
Image Position ◽  
Semi Markov Processes

Our main concern in this paper is the convergence, as t → ∞, of the quantities i, j ∈ E; where Pij(t) is the transition probability of a semi-Markov process whose state space E is irreducible but not closed (i.e., escape from E is possible), and rj is the probability of eventual escape from E conditional on the initial state being i. The theorems proved here generalize some results of Seneta and Vere-Jones ([8] and [11]) for Markov processes.

Additional quasi-stationary distributions for semi-Markov processes

1972 ◽  
Vol 9 (3) ◽  
pp. 671-676 ◽  
Author(s):  
David C. Flaspohler ◽  
Paul T. Holmes
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Initial State ◽  
Stationary Distributions ◽  
Absorbing State ◽  
Semi Markov Process ◽  
Image Position ◽  
Semi Markov Processes

Consider a semi-Markov process X(t) defined on a subset of the non-negative integers with zero as an absorbing state and the non-zero states forming an irreducible class with exit to zero being possible. Conditions are given for the existence of the limits: where Xj(t) is the amount of time prior to time t spent in state j.The limits (which are independent of the initial state) are evaluated when the sufficient conditions are satisfied.

Additional quasi-stationary distributions for semi-Markov processes

1972 ◽  
Vol 9 (03) ◽  
pp. 671-676 ◽  
Author(s):  
David C. Flaspohler ◽  
Paul T. Holmes
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Initial State ◽  
Stationary Distributions ◽  
Absorbing State ◽  
Semi Markov Process ◽  
Image Position ◽  
Semi Markov Processes

Consider a semi-Markov process X(t) defined on a subset of the non-negative integers with zero as an absorbing state and the non-zero states forming an irreducible class with exit to zero being possible. Conditions are given for the existence of the limits: where Xj (t) is the amount of time prior to time t spent in state j. The limits (which are independent of the initial state) are evaluated when the sufficient conditions are satisfied.

scholarly journals Quantum Semi-Markov Processes

2008 ◽  
Vol 101 (14) ◽  
Author(s):  
Heinz-Peter Breuer ◽  
Bassano Vacchini
Keyword(s):  
Markov Processes ◽  
Semi Markov Processes

scholarly journals A continuous-time semi-markov bayesian belief network model for availability measure estimation of fault tolerant systems

2008 ◽  
Vol 28 (2) ◽  
pp. 355-375 ◽  
Author(s):  
Márcio das Chagas Moura ◽  
Enrique López Droguett
Keyword(s):  
Hybrid Model ◽  
Markov Processes ◽  
Continuous Time ◽  
Fault Tolerant ◽  
Numerical Procedure ◽  
Bayesian Belief Networks ◽  
Operational Conditions ◽  
Fault Tolerant Systems ◽  
Semi Markov Processes ◽  
Availability Measure

In this work it is proposed a model for the assessment of availability measure of fault tolerant systems based on the integration of continuous time semi-Markov processes and Bayesian belief networks. This integration results in a hybrid stochastic model that is able to represent the dynamic characteristics of a system as well as to deal with cause-effect relationships among external factors such as environmental and operational conditions. The hybrid model also allows for uncertainty propagation on the system availability. It is also proposed a numerical procedure for the solution of the state probability equations of semi-Markov processes described in terms of transition rates. The numerical procedure is based on the application of Laplace transforms that are inverted by the Gauss quadrature method known as Gauss Legendre. The hybrid model and numerical procedure are illustrated by means of an example of application in the context of fault tolerant systems.

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