A Dam with seasonal input
- 1 June 1994
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 31 (2) , 526-541
- https://doi.org/10.2307/3215043
Abstract
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.Keywords
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