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.