Please use this identifier to cite or link to this item: https://doi.org/10.1239/jap/1245676102
Title: Similar states in continuous-time Markov chains
Authors: Yap, V.B. 
Keywords: Holding time
Lumped Markov chain
Reversibility
Uniformisation
Issue Date: Jun-2009
Citation: Yap, V.B. (2009-06). Similar states in continuous-time Markov chains. Journal of Applied Probability 46 (2) : 497-506. ScholarBank@NUS Repository. https://doi.org/10.1239/jap/1245676102
Abstract: 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. © Applied Probability Trust 2009.
Source Title: Journal of Applied Probability
URI: http://scholarbank.nus.edu.sg/handle/10635/105364
ISSN: 00219002
DOI: 10.1239/jap/1245676102
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