This talk is concerned with nonparametric drift estimation for right-censored diffusion processes. Unlike the classical ergodic framework, which relies on one long trajectory and invariant-law averaging, I work in a copies-based setting with many i.i.d. trajectories observed on a fixed horizon. This observation scheme is natural in applications where many subjects are monitored for a limited time only.

After recalling the statistical effect of right censoring in classical survival analysis, I explain how the diffusion problem can still be treated within a projection least-squares framework. The key point is that, although the usual uncensored contrast is no longer directly observable, a suitable semimartingale identity makes it possible to construct an observable censored counterpart. This yields an adaptive nonparametric estimator of the drift based on censored trajectories only. I will present the main construction, the main statistical results, and numerical illustrations, and conclude with a brief perspective on the multidimensional case.