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2 results

  • A Dam with seasonal input

  • Part of
  • Robert B. Lund
  • Journal:
    Journal of Applied Probability / Volume 31 / Issue 2 / June 1994
    Published online by Cambridge University Press:
    14 July 2016, pp. 526-541
    Print publication:
    June 1994

  • This paper examines the infinitely high dam with seasonal (periodic) Lévy input under the unit release rule. We show that a periodic limiting distribution of dam content exists whenever the mean input over a seasonal cycle is less than 1. The Laplace transform of dam content at a finite time and the Laplace transform of the periodic limiting distribution are derived in terms of the probability of an empty dam. Necessary and sufficient conditions for the periodic limiting distribution to have finite moments are given. Convergence rates to the periodic limiting distribution are obtained from the moment results. Our methods of analysis lean heavily on the coupling method and a stochastic monotonicity result.