Limit Theorems for a Storage Process with a Random Release Rule

Affiliation(s)

Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.

Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.

Abstract

We consider a discrete time Storage Process*X*_{n} with a simple random walk input *S*_{n} and a random release rule given by a family {*U*_{x}, *x* ≥ 0} of random variables whose probability laws {*U*_{x}, *x* ≥ 0} form a convolution semigroup of measures, that is, *μ*_{x} × *μ*_{y} = *μ*_{x + y} The process *X*_{n} obeys the equation: *X*_{0} = 0, *U*_{0} = 0, *X*_{n} = *S*_{n} － *U*_{Sn}, *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.

We consider a discrete time Storage Process

Cite this paper

L. Meziani, "Limit Theorems for a Storage Process with a Random Release Rule,"*Applied Mathematics*, Vol. 3 No. 11, 2012, pp. 1607-1613. doi: 10.4236/am.2012.311222.

L. Meziani, "Limit Theorems for a Storage Process with a Random Release Rule,"

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