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Reversibility and Acyclicity

Published online by Cambridge University Press:  05 September 2017

P. Whittle
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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
Information
Journal of Applied Probability , Volume 12 , Issue S1 , 1975 , pp. 217 - 224
Copyright
Copyright © 1975 Applied Probability Trust 

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References

[1] Bartlett, M. S. (1955) An Introduction to Stochastic Processes. Cambridge University Press.Google Scholar
[2] Kolmogorov, A.N. (1936) Zur Theorie der Markoffschen Ketten. Math. Ann. 112, 155–160.Google Scholar
[3] Whittle, P. (1955) Reversibility in Markov processes. Unpublished manuscript.Google Scholar
[4] Whittle, P. (1965) Statistical processes of aggregation and polymerisation. Proc. Camb. Phil. Soc. 61, 475–495.Google Scholar
[5] Whittle, P. (1965) The equilibrium statistics of a clustering process in the uncondensed phase. Proc. Roy. Soc. A 285, 501–519.Google Scholar