The Annals of Applied Probability

A central limit theorem for stochastic recursive sequences of topical operators

Glenn Merlet

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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.

Article information

Ann. Appl. Probab. Volume 17, Number 4 (2007), 1347-1361.

First available in Project Euclid: 10 August 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 93C65: Discrete event systems 60F05: Central limit and other weak theorems
Secondary: 90B 93B25: Algebraic methods 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

CLT central limit theorem topical functions max-plus mixing stochastic recursive sequences products of random matrices


Merlet, Glenn. A central limit theorem for stochastic recursive sequences of topical operators. Ann. Appl. Probab. 17 (2007), no. 4, 1347--1361. doi:10.1214/105051607000000168.

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