A central limit theorem for stochastic recursive sequences of topical operators
Merlet, Glenn (2007), A central limit theorem for stochastic recursive sequences of topical operators, The Annals of Applied Probability, 17, 4, p. 1347-1361. http://dx.doi.org/10.1214/105051607000000168
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/math/0606668v3
Journal nameThe Annals of Applied Probability
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Abstract (EN)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.
Subjects / KeywordsCLT; central limit theorem; topical functions; max-plus; mixing; stochastic recursive sequences; products of random matrices
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