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K. Yamada, “Diffusion Approximations for Storage Processes with General Release Rules,” Mathematics of Operations Research, Vol. 9, No. 3, 1984, pp. 459-470. doi:10.1287/moor.9.3.459

has been cited by the following article:

• TITLE: Limit Theorems for a Storage Process with a Random Release Rule

  AUTHORS: Lakhdar Meziani

  KEYWORDS: Storage Process; Random Walk; Strong Law of Large Numbers; Central Limit Theorem

  JOURNAL NAME: Applied Mathematics, Vol.3 No.11, November 14, 2012

  ABSTRACT: 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.