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A new covariance inequality and applications

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  • Dedecker, Jérôme
  • Doukhan, Paul

Abstract

We compare three dependence coefficients expressed in terms of conditional expectations, and we study their behaviour in various situations. Next, we give a new covariance inequality involving the weakest of those coefficients, and we compare this bound to that obtained by Rio (Ann. Inst. H. Poincaré Probab. Statist. 29 (1993) 587-597) in the strongly mixing case. This new inequality is used to derive sharp limit theorems, such as Donsker's invariance principle and Marcinkiewicz's strong law. As a consequence of a Burkhölder-type inequality, we obtain a deviation inequality for partial sums.

Suggested Citation

  • Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
    • Handle: RePEc:eee:spapps:v:106:y:2003:i:1:p:63-80
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    References listed on IDEAS

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    1. Esseen, Carl-Gustav & Janson, Svante, 1985. "On moment conditions for normed sums of independent variables and martingale differences," Stochastic Processes and their Applications, Elsevier, vol. 19(1), pages 173-182, February.
    2. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    3. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
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