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August 2007 A central limit theorem for stochastic recursive sequences of topical operators
Glenn Merlet
Ann. Appl. Probab. 17(4): 1347-1361 (August 2007). DOI: 10.1214/105051607000000168

Abstract

Let (An)n∈ℕ be a stationary sequence of topical (i.e., isotone and additively homogeneous) operators. Let x(n, x0) be defined by x(0, x0)=x0 and x(n+1, x0)=Anx(n, x0). It can model a wide range of systems including train or queuing networks, job-shop, timed digital circuits or parallel processing systems.

When (An)n∈ℕ has the memory loss property, (x(n, x0))n∈ℕ satisfies a strong law of large numbers. We show that it also satisfies the CLT if (An)n∈ℕ fulfills the same mixing and integrability assumptions that ensure the CLT for a sum of real variables in the results by P. Billingsley and I. Ibragimov.

Citation

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Glenn Merlet. "A central limit theorem for stochastic recursive sequences of topical operators." Ann. Appl. Probab. 17 (4) 1347 - 1361, August 2007. https://doi.org/10.1214/105051607000000168

Information

Published: August 2007
First available in Project Euclid: 10 August 2007

zbMATH: 1220.60016
MathSciNet: MR2344309
Digital Object Identifier: 10.1214/105051607000000168

Subjects:
Primary: 60F05, 93C65
Secondary: 60J10, 90B, 93B25

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.17 • No. 4 • August 2007
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