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Reversibility and Acyclicity
Published online by Cambridge University Press: 05 September 2017
Abstract
It is well-known that the transition matrix of a reversible Markov process can have only real eigenvalues. An example is constructed which shows that the converse assertion does not hold. A generalised notion of reversibility is proposed, ‘dynamic reversibility’, which has many of the implications for the form of the transition matrix of the classical definition, but which does not exclude ‘circulation in state-space’ or, indeed, periodicity.
- Type
- Part V — Stochastic Processes
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- Copyright © 1975 Applied Probability Trust
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