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Limit Theorems for a Storage Process with a Random Release Rule

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DOI: 10.4236/am.2012.311222    2,694 Downloads   4,203 Views  
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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 = SnUSn, 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.

Conflicts of Interest

The authors declare no conflicts of interest.

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.

References

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