Chebyshev-like inequalities for dam models

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Abstract
A dam model is proposed for which it is assumed that the conditional distributions of the inputs, given the past, are known only to lie in some class M . For selected M , bounds are derived on various quantities of interest such as the mean time to first emptiness. The case of normal inputs is treated in greater detail and a release rule is discussed. The techniques used are similar to those used in the theory of gambling as developed by Dubins and Savage (1965).

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