Circuit Representations of Finite Recurrent Markov Chains

  • Sophia L. Kalpazidou
Part of the Stochastic Modeling and Applied Probability book series (SMAP, volume 28)


In Chapter 2 we have investigated the genesis of finite Markov chains from a collection {𝒞, w c } of directed circuits and positive numbers. We are now interested in the inverse problem: find a class {𝒞, w c } of directed circuits (or cycles) c and positive numbers w c which can describe by either linear or convex expressions the transition probabilities of two finite Markov chains ξ and χ, with reversed parameter-scale and admitting a common invariant probability distribution. The solutions {𝒞, w c } to this problem will be called the circuit (cycle)representation of ξ. In addition, the class {𝒞, w c } will be called either “probabilistic” or “deterministic” (“nonrandomized”) according to whether or not the circuits and their weights enjoy or do not enjoy probabilistic interpretations in terms of the chain ξ.


Markov Chain Distinct Point Betti Number Circuit Representation Stochastic Matrix 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Sophia L. Kalpazidou
    • 1
  1. 1.Department of MathematicsAristotle University of ThessalonikiThessalonikiGreece

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