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A new weak dependence condition and applications to moment inequalities

Listed author(s):
  • Doukhan, Paul
  • Louhichi, Sana
Registered author(s):

    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

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(99)00055-1
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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 84 (1999)
    Issue (Month): 2 (December)
    Pages: 313-342

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    Handle: RePEc:eee:spapps:v:84:y:1999:i:2:p:313-342
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    1. Jakubowski, Adam, 1993. "Minimal conditions in p-stable limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 44(2), pages 291-327, February.
    2. Lanh Tran, 1990. "Recursive kernel density estimators under a weak dependence condition," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 305-329, June.
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