Abstract
What is in this chapter? In Chapters I and II we considered chains that change state at integer times. In this chapter, the change of state occurs after a random time. We are still considering chains with countably many states. Many of the results and techniques of the preceding chapter may be adapted to this new class of models.
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Notes and references
The question of construction of continuous time Markov chains is rather involved and the interested reader should consult more advanced books like Feller (1971) or Bhattacharya and Waymire (1990). The uniqueness of the stationary distribution (when it exists) does not always hold if the chain is on an uncountable set. See the voter model or the contact process in Liggett (1985) or Durrett (1988). We have treated a very particular queue which is not Markovian in Section 7, for more on this see for instance Grimmett and Stirzaker (1992).
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© 1999 Springer Science+Business Media New York
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Schinazi, R.B. (1999). Continuous Time Birth and Death Markov Chains. In: Classical and Spatial Stochastic Processes. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1582-0_3
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DOI: https://doi.org/10.1007/978-1-4612-1582-0_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7203-8
Online ISBN: 978-1-4612-1582-0
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