Numerical Method for Bounds Computations of Discrete-Time Markov Chains with Different State Spaces

Authors:
Mourad Ahmane;Laurent Truffet
Affiliations:
SET Laboratory, University of Technology of Belfort-Montbéliard, Belfort, France 90010;Ecole des Mines de Nantes, Nantes Cedex3, France 44307
Venue:
ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
Year:
2009

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Abstract

In this paper, we propose a numerical method for bounds computations of discrete-time Markov chains with different state spaces. This method is based on the necessary and sufficient conditions for the comparison of one-dimensional (also known as the point-wise comparison) of discrete-time Markov chains given in our previous work [3]. For achieving our objective, we proceed as follows. Firstly, we transform the comparison criterion under the form of a complete linear system of inequalities. Secondly, we use our implementation on Scilab software of Gamma-algorithm to determine the set of all possible bounds of a given Markov chain.