Infinite dams with discrete additive inputs

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Abstract
This paper considers an infinite dam fed by a discrete input Xt during the time interval [t, t + 1), t = 0, 1, 2, ···. At time t – 0 there is an output Yt = min(Zt –1, + Xt –1, r) from the dam leaving behind the amount Zt = max(0, Zt –1, + Xt –1, r). The probability Pr(Zt = i), i = 0, 1, 2, ··· is discussed under the strict assumption that r > 1 and the given initial condition that Z 0 = u, u = 1, 2, ···. The generating function technique has been used throughout the paper.

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