Vitesses optimale et suroptimale des polygones de fréquences pour les processus à temps continu

This Note deals with density estimation in continuous-time. Then under mild regularity and asymptotic independence conditions, the mean integrated square error achieves the same optimal rate T−4/5 of convergence to zero as in the i.i.d. case. Under a local assumption weaker than Castellana-Leadbetter's [Stochastic Process. Appl. 21 (1986) 179-193], we obtain the parametric rate T−1. To cite this article: F.-X. Lejeune, C. R. Acad. Sci. Paris, Ser. I 341 (2005).