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- W1568310689 abstract "We consider a multidimensional elliptic diffusion Xα,β, whose drift b(α,x) and diffusion coefficients S(β,x) depend on multidimensional parameters α and β. We assume some various hypotheses on b and S, which ensure that Xα,β is ergodic, and we address the problem of the validity of the Local Asymptotic Normality (LAN in short) property for the likelihoods, when the sample is (XkΔn)0⩽k⩽n, under the conditions Δn→0 and nΔn→+∞. We prove that the LAN property is satisfied, at rate nΔn for α and n for β: our approach is based on a Malliavin calculus transformation of the likelihoods. Nous considèrons un processus de diffusion multidimensionnel elliptique Xα,β, dont les coefficients de dérive b(α,x) et de diffusion S(β,x) dépendent de paramètres multidimensionnels α et β. Nous formulons plusieurs jeux d'hypothèses sur b and S, assurant l'ergodicité de Xα,β, et nous nous intéressons à la validité de la propriété LAN (Local Asymptotic Normality) pour les vraisemblances, quand l'échantillon observé est (XkΔn)0⩽k⩽n, sous les conditions Δn→0 et nΔn→+∞. Nous démontrons que la proprièté LAN est vérifiée, avec les vitesses nΔn pour α et n pour β : notre approche repose sur une réécriture du rapport de vraisemblance à l'aide du calcul de Malliavin." @default.
- W1568310689 created "2016-06-24" @default.
- W1568310689 creator A5078591220 @default.
- W1568310689 date "2002-01-01" @default.
- W1568310689 modified "2023-10-09" @default.
- W1568310689 title "Propriété LAN pour les diffusions ergodiques avec observations discrètes" @default.
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- W1568310689 doi "https://doi.org/10.1016/s0246-0203(02)01107-x" @default.
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