Convergence des moments dans le théorème de la limite centrale presque sûr pour les martingales vectorielles

BERCU, Bernard; CÉNAC, Peggy; FAYOLLE, Guy

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BERCU, Bernard
Institut de Mathématiques de Bordeaux [IMB]

CÉNAC, Peggy
Mathématiques Appliquées Paris 5 [MAP5 - UMR 8145]

FAYOLLE, Guy
Probability, modelling and evaluation of information processing systems [PREVAL]

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Ce document a été publié dans

2006p. 21

Résumé en anglais

In this report, new almost sure convergence properties for vectorial martingale transforms are established. Assuming some regularity conditions both on the increasing process and on the moments of the martingale, one can show that normalized moments of any even order do also converge in the almost sure cental limit theorem for martingales. Firm conjectures are proposed to relax some of the hypotheses, the goal being to cover a much wider class of processes. Cases studies are proposed, including linear models and some branching processes, where new asymptotic estimation and prediction errors are obtained.< Réduire

Mots clés en anglais

vectorial martingale

Almost sure cental limit theorem

moment

regression

vectorial martingale.

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