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May, 1985 A Limit Theorem for Nonnegative Additive Functionals of Storage Processes
Keigo Yamada
Ann. Probab. 13(2): 397-413 (May, 1985). DOI: 10.1214/aop/1176992999


We consider a storage process $X(t)$ having a compound Poisson process as input and general release rules, and a nonnegative additive functional $Z(t) = \int^t_0 f(X(s)) ds$. Under the situation that the input rate is equal to the maximal output rate, it is shown for a suitable class of functions of $f$ that an appropriate normalization of the process $Z(t)$ converges weakly to a process which is represented as a constant times the local time of a Bessel process at zero.


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Keigo Yamada. "A Limit Theorem for Nonnegative Additive Functionals of Storage Processes." Ann. Probab. 13 (2) 397 - 413, May, 1985.


Published: May, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0571.60045
MathSciNet: MR781413
Digital Object Identifier: 10.1214/aop/1176992999

Primary: 60F17
Secondary: 60J55 , 60K30

Keywords: Functional limit theorem , local time of Bessel process , storage process

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 2 • May, 1985
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