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1 results

  • Extended continued fractions, recurrence relations and two-dimensional Markov processes

  • C. E. M. Pearce
  • Journal:
    Advances in Applied Probability / Volume 21 / Issue 2 / June 1989
    Published online by Cambridge University Press:
    01 July 2016, pp. 357-375
    Print publication:
    June 1989

  • Connections between Markov processes and continued fractions have long been known (see, for example, Good [8]). However the usefulness of extended continued fractions in such a context appears not to have been explored. In this paper a convergence theorem is established for a class of extended continued fractions and used to provide well-behaved solutions for some general order linear recurrence relations such as arise in connection with the equilibrium distribution of state for some Markov processes whose natural state spaces are of dimension 2. Specific application is made to a multiserver version of a queueing problem studied by Neuts and Ramalhoto [13] and to a model proposed by Cohen [5] for repeated call attempts in teletraffic.