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CLOSED-FORM STOCHASTIC BOUNDS ON THE STATIONARY DISTRIBUTION OF MARKOV CHAINS
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SAINT-W '05 Proceedings of the 2005 Symposium on Applications and the Internet Workshops
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In this article we first give a characterization of a class of probability transition matrices having closed-form solutions for transient distributions and the steady-state distribution. We propose to apply the stochastic comparison approach to construct bounding chains belonging to this class. Therefore, bounding chains can be analyzed efficiently through closed-form solutions in order to provide bounds on the distributions of the considered Markov chain. We present algorithms to construct upper-bounding matrices in the sense of the ≤st and ≤icx order.