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February 1997 A law of large numbers on randomly deleted sets
Mark D. Rothmann, Ralph P. Russo
Ann. Appl. Probab. 7(1): 170-182 (February 1997). DOI: 10.1214/aoap/1034625258


Consider a system into which units having random magnitude enter at arbitrary times and remain "active" (present in the system) for random periods. Suppose units of high magnitude have stochastically greater lifetimes (tend to stay active for longer periods) than units of low magnitude. Of interest is the process ${\mu (t): t \geq 0}$ where $\mu (t)$ denotes the average magnitude of all units active at time t. We give conditions which guarantee the convergence of $\mu (t)$ and we determine the form of the limit. Some related processes are also studied.


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Mark D. Rothmann. Ralph P. Russo. "A law of large numbers on randomly deleted sets." Ann. Appl. Probab. 7 (1) 170 - 182, February 1997.


Published: February 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0878.60027
MathSciNet: MR1428755
Digital Object Identifier: 10.1214/aoap/1034625258

Primary: 60F15
Secondary: 60G17

Keywords: random deletion , sample means , SLLN

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.7 • No. 1 • February 1997
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