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Asymptotic distribution of the maximum deficit with correlated, partially regulated outflows

Brent M. Troutman
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Abstract

The asymptotic distribution of the maximum accumulated deficit with partially regulated, Markov-dependent net outflows having a Bernoulli distribution is derived, and the distribution for independent, continuous outflows is presented. It is demonstrated that under partial regulation the maximum deficit behaves as log n , where n is the length of the series; this is to be contrasted with the n ½ behavior exhibited by fully regulated outflows. Also, as would be expected, the presence of correlation tends to increase the magnitude and variability of the maximum deficit.

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Brent M. Troutman. 2010-07-09. Asymptotic distribution of the maximum deficit with correlated, partially regulated outflows. https://doi.org/10.1029/wr019i001p00104

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