Bounds and approximations for continuous-time Markovian transition probabilities and large systems

We propose new bounds and approximations for the transition probabilities of a continuous-time Markov process with finite but large state-space. The bounding and approximating procedures have been exposed in another paper [S. Mercier, Numerical bounds for semi-Markovian quantities and applications t...

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Bibliographic Details
Published in:European journal of operational research Vol. 185; no. 1; pp. 216 - 234
Main Author: Mercier, Sophie
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.02.2008
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Algorithms
Applied sciences
Approximation
Eulers equations
Exact sciences and technology
Finite volume method
Markov analysis
Markov processes
Mathematics
Numerical bounds and approximations
Operational research and scientific management
Operational research. Management science
Probability
Reliability
Reliability theory. Replacement problems
Studies
Time-dependent quantities
Markov processes
Numerical bounds and approximations
Reliability
Time-dependent quantities
Markov process
Euler equation
Probabilistic approach
Finite volume method
Continuous time
State space
State space method
Numerical approximation
Continuous process
Time dependence
Marginal distribution
Transition probability
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:We propose new bounds and approximations for the transition probabilities of a continuous-time Markov process with finite but large state-space. The bounding and approximating procedures have been exposed in another paper [S. Mercier, Numerical bounds for semi-Markovian quantities and applications to reliability, in revision for Methodology and Computing in Applied Probability] in the more general context of a continuous-time semi-Markov process with countable state-space. Such procedures are here specialized to the Markovian finite case, leading to much simpler algorithms. The aim of this paper is to test such algorithms versus other algorithms from the literature near from ours, such as forward Euler approximation, external uniformization and a finite volume method from [C. Cocozza-Thivent, R. Eymard, Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme, ESAIM: M2AN 38(5) (2004) 853–875].
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2006.12.036