Maximum spacing estimation for continuous time Markov chains and semi-Markov processes

2021 ◽  
Author(s):  
Kristi Kuljus ◽  
Bo Ranneby
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Continuous Time ◽  
Continuous Time Markov Chains ◽  
Semi Markov Processes

scholarly journals Maximal Coupling Procedure and Stability of Continuous-Time Markov Chains

2014 ◽  
Vol 10 ◽  
pp. 30-37
Author(s):  
Mokaedi V. Lekgari
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Continuous Time ◽  
Stopping Times ◽  
Continuous Time Markov Chains ◽  
Maximal Coupling ◽  
Countable State ◽  
Coupling Procedure ◽  
The Stability

In this study we first investigate the stability of subsampled discrete Markov chains through the use of the maximal coupling procedure. This is an extension of the available results on Markov chains and is realized through the analysis of the subsampled chain ΦΤn, where {Τn, nєZ+}is an increasing sequence of random stopping times. Then the similar results are realized for the stability of countable-state Continuous-time Markov processes by employing the skeleton-chain method.

A SUCCESSIVE LUMPING PROCEDURE FOR A CLASS OF MARKOV CHAINS

2012 ◽  
Vol 26 (4) ◽  
pp. 483-508 ◽  
Author(s):  
Michael N. Katehakis ◽  
Laurens C. Smit
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Queueing Models ◽  
Semi Markov Processes ◽  
Stationary Probabilities

A class of Markov chains we call successively lumbaple is specified for which it is shown that the stationary probabilities can be obtained by successively computing the stationary probabilities of a propitiously constructed sequence of Markov chains. Each of the latter chains has a(typically much) smaller state space and this yields significant computational improvements. We discuss how the results for discrete time Markov chains extend to semi-Markov processes and continuous time Markov processes. Finally, we will study applications of successively lumbaple Markov chains to classical reliability and queueing models.

A description of the long-term behaviour of absorbing continuous-time Markov chains using a centre manifold

1990 ◽  
Vol 22 (1) ◽  
pp. 111-128 ◽  
Author(s):  
P. K. Pollett ◽  
A. J. Roberts
Keyword(s):  
Differential Equations ◽  
Markov Chains ◽  
Invariant Manifold ◽  
Markov Processes ◽  
Continuous Time ◽  
Transition Probabilities ◽  
Centre Manifold ◽  
Continuous Time Markov Chains ◽  
Linear Differential

We use the notion of an invariant manifold to describe the long-term behaviour of absorbing continuous-time Markov processes with a denumerable infinity of states. We show that there exists an invariant manifold for the forward differential equations and we are able to describe the evolution of the state probabilities on this manifold. Our approach gives rise to a new method for calculating conditional limiting distributions, one which is also appropriate for dealing with processes whose transition probabilities satisfy a system of non-linear differential equations.

A description of the long-term behaviour of absorbing continuous-time Markov chains using a centre manifold

1990 ◽  
Vol 22 (01) ◽  
pp. 111-128 ◽  
Author(s):  
P. K. Pollett ◽  
A. J. Roberts
Keyword(s):  
Differential Equations ◽  
Markov Chains ◽  
Invariant Manifold ◽  
Markov Processes ◽  
Continuous Time ◽  
Transition Probabilities ◽  
Centre Manifold ◽  
Continuous Time Markov Chains ◽  
Linear Differential

We use the notion of an invariant manifold to describe the long-term behaviour of absorbing continuous-time Markov processes with a denumerable infinity of states. We show that there exists an invariant manifold for the forward differential equations and we are able to describe the evolution of the state probabilities on this manifold. Our approach gives rise to a new method for calculating conditional limiting distributions, one which is also appropriate for dealing with processes whose transition probabilities satisfy a system of non-linear differential equations.

First-passage-time moments of Markov processes

1985 ◽  
Vol 22 (4) ◽  
pp. 939-945 ◽  
Author(s):  
David D. Yao
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Continuous Time ◽  
Fundamental Matrix ◽  
Generalized Inverse ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Continuous Time Markov Chains ◽  
Passage Times

We consider the first-passage times of continuous-time Markov chains. Based on the approach of generalized inverse, moments of all orders are derived and expressed in simple, explicit forms in terms of the ‘fundamental matrix'. The formulas are new and are also efficient for computation.

Stochastic ordering for continuous-time processes

2003 ◽  
Vol 40 (2) ◽  
pp. 361-375 ◽  
Author(s):  
A. Irle
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Stochastic Ordering ◽  
Level Crossing ◽  
Birth And Death Processes ◽  
Wiener Processes ◽  
Continuous Time Processes ◽  
Semi Markov Processes

We consider the following ordering for stochastic processes as introduced by Irle and Gani (2001). A process (Yt)t is said to be slower in level crossing than a process (Zt)t if it takes (Yt)t stochastically longer than (Zt)t to exceed any given level. In Irle and Gani (2001), this ordering was investigated for Markov chains in discrete time. Here these results are carried over to semi-Markov processes with particular attention to birth-and-death processes and also to Wiener processes.

First-passage-time moments of Markov processes

1985 ◽  
Vol 22 (04) ◽  
pp. 939-945
Author(s):  
David D. Yao
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Continuous Time ◽  
Fundamental Matrix ◽  
Generalized Inverse ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Continuous Time Markov Chains ◽  
Passage Times

We consider the first-passage times of continuous-time Markov chains. Based on the approach of generalized inverse, moments of all orders are derived and expressed in simple, explicit forms in terms of the ‘fundamental matrix'. The formulas are new and are also efficient for computation.

Stochastic ordering for continuous-time processes

2003 ◽  
Vol 40 (02) ◽  
pp. 361-375 ◽  
Author(s):  
A. Irle
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Stochastic Ordering ◽  
Level Crossing ◽  
Birth And Death Processes ◽  
Wiener Processes ◽  
Continuous Time Processes ◽  
Semi Markov Processes

We consider the following ordering for stochastic processes as introduced by Irle and Gani (2001). A process (Y t ) t is said to be slower in level crossing than a process (Z t ) t if it takes (Y t ) t stochastically longer than (Z t ) t to exceed any given level. In Irle and Gani (2001), this ordering was investigated for Markov chains in discrete time. Here these results are carried over to semi-Markov processes with particular attention to birth-and-death processes and also to Wiener processes.

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