%0 Journal Article
%T Limit Theorems for a Storage Process with a Random Release Rule
%A Lakhdar Meziani
%J Applied Mathematics
%P 1607-1613
%@ 2152-7393
%D 2012
%I Scientific Research Publishing
%R 10.4236/am.2012.311222
%X We consider a discrete time Storage Process <i>X<sub>n</sub></i> with a simple random walk input <i>S<sub>n</sub></i> and a random release rule given by a family {<i>U<sub>x</sub></i>, <i>x</i> ¡Ý 0} of random variables whose probability laws {<i>U<sub>x</sub></i>, <i>x</i> ¡Ý 0} form a convolution semigroup of measures, that is, <i>¦Ì<sub>x</sub></i> ¡Á <i>¦Ì<sub>y</sub></i> = <i>¦Ì<sub>x + y</sub></i> The process <i>X<sub>n</sub></i> obeys the equation: <i>X</i><sub>0</sub> = 0, <i>U</i><sub>0</sub> = 0, <i>X<sub>n</sub></i> = <i>S<sub>n</sub></i> £­ <i>U<sub>S<sub>n</sub></sub></i>, <i>n</i> ¡Ý 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.
%K Storage Process
%K Random Walk
%K Strong Law of Large Numbers
%K Central Limit Theorem
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=24377