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Title: Computing the periodicity of finite Markov chains
Authors: Jarvis, James P.
Shier, Douglas R.
Keywords: Markov chain
State transition diagram
Breadth-first search
Issue Date: Jul-1993
Series/Report no.: Research Centre Publications 93-06
Abstract: Determining the period of a finite irreducible Markov chains involves finding the greatest common divisor of the number of transitions that carry any state back to itself with non-zero probability. This is equivalent to finding the greatest common divisor of the lengths of all cycles in the directed graph defined by the state transition diagram. A linear-time algorithm based on a breadth-first search of this directed graph can be used to determine the period of the chain without examining all cycles in the graph.
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