arXiv subjects

Faouzi Chaabane

Publications and source records attributed to Faouzi Chaabane.

2 recordsLinked to original sources

arXiv2006

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

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.

math.PR↗

arXiv2006

Theorems Limit With Weight For The Vectorial Martingales To Continuous Time

We develop a general approach of the almost sure central limit theorem for the quasi-continuous vectorial martingales and we release a quadratic extension of this theorem while specifying speeds of convergence. As an application of this result we study the problem of estimate the variance of a process with stationary and idependent increments in statistics.

math.PR↗