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1 results

  • Birth-and-death processes on the integers with phases and general boundaries

  • Bruce Hajek
  • Journal:
    Journal of Applied Probability / Volume 19 / Issue 3 / September 1982
    Published online by Cambridge University Press:
    14 July 2016, pp. 488-499
    Print publication:
    September 1982

  • The invariant probability distribution is found for a class of birth-and-death processes on the integers with phases and one or two boundaries. The invariant vector has a matrix geometric form and is found by solving a non-linear matrix equation and then finding an invariant probability distribution on the boundary states. Levy's concept of watching a Markov process in a subset is used to naturally decouple the computation of distributions on the boundary and interior states.