 Discrete dams with Markovian inputsAnthony G. Pakes Stochastic Processes and their Applications, 1981, vol. 11, issue 1, 57-77 Abstract: It is known that, subject to some technical conditions, the deficit process of an infinitely deep dam with a Markov chain input process and unit withdrawals has a limiting zero-modified geometric distribution. In this paper it is shown that, provided the state space of the input process is finite, the limiting distribution of the deficit process of a finite dam tends to the zero-modified distribution above as the capacity tends to infinity. A convergence rate is established when the input process is an independent sequence. When the input process is a semi-Markov chain we find a simple condition ensuring that the limiting deficit distribution is a zero-modified geometric distribution. Some results are obtained for infinitely deep, and high, dams when the input process is a first order discrete autoregressive process. Nearly all examples of Markovian input processes have linear conditional expectations. The final section is a brief expository essay on such processes and mentions some open problems. Keywords: Infinitely deep dam infinitely high dam Markov input semi-Markov input discrete auto-regressive input; linearly regressive process branching process with immigration canonical expansion (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:11:y:1981:i:1:p:57-77 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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