Almost sure convergence for iterated functions of independent random variables

• 成果类型: Article
• 署名作者: Jordan, J
• 署名单位: University of Oxford
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2002
• 页码: 985-1000
• 关键词: RENORMALIZATION; conductivity; lattices

摘要

We consider a class of probabilistic models obtained by iterating random functions of k random variables. We prove an analogue of the weak law of large numbers and under a symmetry condition we prove a strong law. The symmetry condition is satisfied if the initial random variables are exchangeable. Our results can be used to give stronger results than those previously obtained in the special case where the function is deterministic. Both types of models have applications in physics and in computer science.