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On the behaviour of a long cascade of linear reservoirs
Published online by Cambridge University Press: 14 July 2016
Abstract
This paper describes the limiting asymptotic behaviour of a long cascade of linear reservoirs fed by stationary inflows into the first reservoir. We show that the storage in the nth reservoir becomes asymptotically deterministic as n → ∞, and establish a central limit theorem for the random fluctuations about the deterministic approximation. In addition, we prove a large deviations theorem that provides precise logarithmic asymptotics for the tail probabilities associated with the storage in the nth reservoir when n is large.
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- Research Papers
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- Copyright © by the Applied Probability Trust 2000
Footnotes
This research was supported by the US Army Research Office under contract no. DAAG55-97-1-0377 and by the National Science Foundation under grant no. DMS-9704732.