Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Asymptotic equivalence for a null recurrent diffusion

Auteur(s):

Code(s) de Classification MSC:

• 62G99 None of the above but in this section
• 62M99 None of the above but in this section

Résumé: We establish that the model generated by the observation of the path of a 1-dimensional null recurrent diffusion, when the parameter is the compactly supported drift, is asymptotically equivalent to a mixed Gaussian white noise experiment as the observation time $T \rightarrow \infty$. The approximation is given in the sense of Le Cam's deficiency $\Delta$-distance over Sobolev balls of smoothness order $\beta > \frac{1}{2}$.

Mots Clés: Nonparametric experiments ; deficiency distance ; diffusion processes ; mixed Gaussian white noise ; mixed normality

Date: 2000-02-18

Prépublication numéro: PMA-567