A new covariance inequality and applications

Jérôme Dedecker and Paul Doukhan

Stochastic Processes and their Applications, 2003, vol. 106, issue 1, 63-80

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.

Keywords: Weak; dependence; Mixingales; Strong; mixing; Covariance; inequalities; Weak; invariance; principle; Moment; inequalities (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (36)

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