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Les champs aléaotoires à longue mémoire

Abstract : We study stationary, second order random fields on the lattice Z^d. They are assumed to be strongly dependent in the sense that their covariance function is not summable. In this investigation and contrary to the previous studies, the long memory can be anisotropic. Assuming the linearity of these random fields allows us to prove the functional convergence of their partial sums. Thanks to this result, we present a testing procedure for long memory of a random field. Besides, we prove the asymptotic degeneracy of the empirical process of long memory random fields ; this yields some statistical application so as the asymptotic behaviour of U-statistics. Finally, we investigate some quadratic forms of long memory random fields : their study is a first step towards the study of the Whittle estimator of the long memory parameters ; moreover, as a first application, we obtain the asymptotic law of the empirical covariances.
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Contributor : Frédéric Lavancier Connect in order to contact the contributor
Submitted on : Monday, March 27, 2006 - 7:05:54 PM
Last modification on : Friday, August 5, 2022 - 2:49:41 PM
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  • HAL Id : tel-00012045, version 1



Frédéric Lavancier. Les champs aléaotoires à longue mémoire. Mathématiques [math]. Université des Sciences et Technologie de Lille - Lille I, 2005. Français. ⟨tel-00012045⟩



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