Markov Processes in Continuous Time

2015 ◽  
pp. 79-123
Author(s):  
Anton Bovier ◽  
Frank den Hollander
Keyword(s):  
Markov Processes ◽  
Continuous Time

Non-ergodicity criteria for denumerable continuous time Markov processes

2004 ◽  
Vol 32 (6) ◽  
pp. 574-580 ◽  
Author(s):  
Bong Dae Choi ◽  
Bara Kim
Keyword(s):  
Markov Processes ◽  
Continuous Time

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.

Markovian manpower models in continuous time

1977 ◽  
Vol 14 (02) ◽  
pp. 249-259 ◽  
Author(s):  
Alexander Mehlmann
Keyword(s):  
Markov Processes ◽  
Continuous Time ◽  
Asymptotic Form ◽  
New Approach ◽  
Limiting Behaviour

The problem of determining the asymptotic form of the stock vector n (t) in a continuous time Markovian manpower model is solved for asymptotically exponential recruitment functions {R(t)}. A new approach to the limiting behaviour of some manpower systems with given total sizes {N(t)} is then given by means of time-inhomogeneous Markov processes.

Proportional intensities and strong ergodicity for Markov processes

1983 ◽  
Vol 20 (01) ◽  
pp. 185-190 ◽  
Author(s):  
Mark Scott ◽  
Dean L. Isaacson
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Homogeneous Markov Process ◽  
Strong Ergodicity ◽  
Transition Functions ◽  
The Matrix ◽  
Intensity Functions ◽  
Time Point

By assuming the proportionality of the intensity functions at each time point for a continuous-time non-homogeneous Markov process, strong ergodicity for the process is determined through strong ergodicity of a related discrete-time Markov process. For processes having proportional intensities, strong ergodicity implies having the limiting matrix L satisfy L · P(s, t) = L, where P(s, t) is the matrix of transition functions.

Homecomings of Markov processes

1973 ◽  
Vol 5 (01) ◽  
pp. 66-102 ◽  
Author(s):  
J. F. C. Kingman
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Continuous Time ◽  
Random Time ◽  
Random Set ◽  
Theoretical Interest ◽  
Different Types ◽  
Treat All ◽  
Image Position

Ifx0is a particular state for a continuous-time Markov processX, the random time setis often of both practical and theoretical interest. Ignoring trivial or pathological cases, there are four different types of structure which this random set can display. To some extent, it is possible to treat all four cases in a unified way, but they raise different questions and require different modes of description. The distributions of various random quantities associated withcan be related to one another by simple and useful formulae.

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