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1 results

  • Similar States in Continuous-Time Markov Chains

  • Part of
  • V. B. Yap
  • Journal:
    Journal of Applied Probability / Volume 46 / Issue 2 / June 2009
    Published online by Cambridge University Press:
    14 July 2016, pp. 497-506
    Print publication:
    June 2009
    • Article
      • You have access
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  • In a homogeneous continuous-time Markov chain on a finite state space, two states that jump to every other state with the same rate are called similar. By partitioning states into similarity classes, the algebraic derivation of the transition matrix can be simplified, using hidden holding times and lumped Markov chains. When the rate matrix is reversible, the transition matrix is explicitly related in an intuitive way to that of the lumped chain. The theory provides a unified derivation for a whole range of useful DNA base substitution models, and a number of amino acid substitution models.