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1 results

  • A note on the infinitely deep dam with a Markovian input

  • R. M. Phatarfod
  • Journal:
    Journal of Applied Probability / Volume 16 / Issue 4 / December 1979
    Published online by Cambridge University Press:
    14 July 2016, pp. 917-922
    Print publication:
    December 1979

  • In this paper we consider an infinitely deep dam fed by inputs which form an ergodic Markov chain and whose release M is non-unit. The extension to non-unit release follows on lines similar to the independent inputs case. We show that P(θ) – θ MΙ where P(θ) = (pijθ i) has a maximum of N = M(M + l)/2 non-zero singularities in the unit disc, so that the general solution of the equilibrium equations has N unknown constants. We also show that these constants satisfy N linear constraints, so that the solution is fully determined.