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.
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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.
Publié le : 2007-08-14
Classification:
CLT,
central limit theorem,
topical functions,
max-plus,
mixing,
stochastic recursive sequences,
products of random matrices,
93C65,
60F05,
90B,
93B25,
60J10
@article{1186755242,
author = {Merlet, Glenn},
title = {A central limit theorem for stochastic recursive sequences of topical operators},
journal = {Ann. Appl. Probab.},
volume = {17},
number = {1},
year = {2007},
pages = { 1347-1361},
language = {en},
url = {http://dml.mathdoc.fr/item/1186755242}
}
Merlet, Glenn. A central limit theorem for stochastic recursive sequences of topical operators. Ann. Appl. Probab., Tome 17 (2007) no. 1, pp. 1347-1361. http://gdmltest.u-ga.fr/item/1186755242/