Abstract
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).
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