An Asymptotic Theory for Dams

Abstract

IN my contribution to the discussion at a symposium¹ in 1957 on the theory of dams, I suggested that the distribution of the time to emptiness of a finite dam or reservoir might be investigated by the use of Wald's identity. This method has recently been used by R. M. Phatarfod² in the case of inputs with negative exponential distribution. It seems worth noting how the asymptotic case of normal diffusion, which should be useful as an approximation in all cases where individual (independent) increments are fairly small in relation to the capacity of the dam, may be dealt with. This asymptotic theory has, moreover, an immediate extension to the case of correlated increments by our determining the effective diffusion per unit time in such a case (compare with my concluding remarks, loc. cit.).