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

Abstract

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 $σ^{2}$ 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.