Two Problems in Markov Chains: A Topological Approach

G. Guardabassi and S. Rinaldi
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G. Guardabassi: Istituto di Elettrotecnica ed Elettronica, Politecnico of Milan, Italy
S. Rinaldi: Istituto di Elettrotecnica ed Elettronica, Politecnico of Milan, Italy

Operations Research, 1970, vol. 18, issue 2, 324-333

Abstract: This paper deals with two problems of asymptotic aggregation of an ergodic Markov chain. The first is concerned with the determination of an aggregated Markov chain, the asymptotic probabilities of which are just equal to conditional asymptotic probabilities defined on the original Markov chain. The second one relates to the determination of an aggregated chain, the asymptotic probabilities of which are equal to the asymptotic probabilities of the elements of a given state partition. Both problems are approached from a topological point of view and solutions are given in terms of signal-flow graph techniques. Comments about the main computational features of the method are also included.

Date: 1970
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