A central limit theorem for stochastic recursive sequences of topical operators

• 成果类型: Article
• 署名作者: Merlet, Glenn
• 署名单位: Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051607000000168
• 发表日期: 2007
• 页码: 1347-1361
• 关键词: random matrices; systems; PRODUCTS; networks; Algebra; events

摘要

Let (A(n))(n is an element of N) be a stationary sequence of topical (i.e., isotone and additively homogeneous) operators. Let x (n, x(0)) be defined by x (0, x(0)) = x(0) and x (n + 1, x(0)) = A(n)x (n, x(0)). It can model a wide range of systems including train or queuing networks, job-shop, timed digital circuits or parallel processing systems. When (A(n))(n is an element of N) has the memory loss property, (x (n, x(0)))(n is an element of N) satisfies a strong law of large numbers. We show that it also satisfies the CLT if (A(n))(n is an element of 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.