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Moderate deviations principles for self-normalized martingales

Abstract : We prove, for martingales self-normalized by their increasing process, the upper bound of a moderate deviations principle. Self-normalizing allows to get rid of the of exponential convergence of the previsible square variation which appears in previous works on a deterministic normalization of the martingale. The proof relies on the notion of partial large deviations principle introduced by Dembo and Shao in [3] and [4]. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
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Submitted on : Wednesday, May 2, 2012 - 11:35:09 PM
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J Worms. Moderate deviations principles for self-normalized martingales. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2000, 330 (10), pp.909--914. ⟨10.1016/S0764-4442(00)00284-6⟩. ⟨hal-00693779⟩

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