Statistiques de diffusions et temps local. (Statistics of diffusions and local times)
Consider a real-valued diffusion process the diffusion and drift coefficients of which are respectively a constant number and a function depending on some unknown parameter \(\theta\). Suppose moreover that we do not observe completely the diffusion but only its zero crossing times after excursions longer than some \(\epsilon\). We want to estimate \(\theta\) ; this work provides us with a systematic statistical study of this problem. A quasi-likelihood is introduced and the asymptotic properties of the estimators as the time goes to infinity are proved: consistency, asymptotic normality.
scientific article; zbMATH DE number 4036976