We consider a discrete time Storage Process Xn with a simple random walk input Sn and a random release rule given by a family {Ux, x ≥ 0} of random variables whose probability laws {Ux, x ≥ 0} form a convolution semigroup of measures, that is, μx × μy = μx + y The process Xn obeys the equation: X0 = 0, U0 = 0, Xn = Sn － USn, n ≥ 1. Under mild assumptions, we prove that the processes and are simple random walks and derive a SLLN and a CLT for each of them.
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