A new weak dependence condition and applications to moment inequalities

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• 作者：Doukhan ; Paul ; Louhichi ; Sana
• 关键词：60E15 ; 60F05 ; 60F17 ; 60G10 ; 60G99 ; Stationary sequences ; Inequalities ; Rosenthal inequality ; Positive dependence ; Mixing ; Central Limit Theorem
• 刊名：Stochastic Processes and their Applications
• 出版年：1999
• 出版时间：December 1, 1999
• 年：1999
• 卷：84
• 期：2
• 页码：313-342
• 全文大小：215 K

文摘

The purpose of this paper is to propose a unifying weak dependence condition. Mixing sequences, functions of associated or Gaussian sequences, Bernoulli shifts as well as models with a Markovian representation are examples of the models considered. We establish Marcinkiewicz–Zygmund, Rosenthal and exponential inequalities for general sequences of centered random variables. Inequalities are stated in terms of the decay rate for the covariance of products of the initial random variables subject to the condition that the gap of time between both products tends to infinity. As applications of those notions, we obtain a version of the functional CLT and an invariance principle for the empirical process