Identification d'un processus autorégressif gaussien stable par la méthode de moyennisation logarithmique

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In the present work, we consider a stable one-dimensional gaussian autoregressive model in continous time. Using the limit theorems with logarithmic averaging obtained for continous local martingales, we construct then an estimator of the noise covariance σ² and an estimator of θ different of the one of the least squares estimator. By exploiting the weighting method we ameliorate the convergence rates of these new estimators.