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More on Time-Reversibility; Potential Coefficients; Process Modification

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Markov Chain Models — Rarity and Exponentiality

Part of the book series: Applied Mathematical Sciences ((AMS,volume 28))

Abstract

The significance of the presence of time-reversibility for applied models is emphasized; namely their tractability, the accessibility of their ergodic state probabilities, and the simplicity of their time dependent behavior. The spectral representation of the transition probability matrix p(t) is established, and its structure explored. For timereversible processes, a key property of path independence is present which permits extension of the notion of time-reversibility to transient chains and “lossy” chains. Time-reversible processes may be modified in a variety of ways without destroying the reversibility. The modified process is often of interest in its own right or is of primary interest. The last section introduces replacement processes, of special interest.

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© 1979 Springer-Verlag New York Inc.

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Keilson, J. (1979). More on Time-Reversibility; Potential Coefficients; Process Modification. In: Keilson, J. (eds) Markov Chain Models — Rarity and Exponentiality. Applied Mathematical Sciences, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6200-8_4

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  • DOI: https://doi.org/10.1007/978-1-4612-6200-8_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90405-4

  • Online ISBN: 978-1-4612-6200-8

  • eBook Packages: Springer Book Archive

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