A central limit theorem for stochastic recursive sequences of topical operators

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.