Truncated dynamics and estimation of diffusion equations

We study inference on continuous-time processes from discrete data with a g iven time interval between consecutive observations, and propose a modifica tion of the sieve estimation method based on the infinitesimal generator. O ur approach consists on truncating the initial process to improve the estim ation of the eigenfunctions at the boundaries of the set of admissible valu es. For diffusion processes, nonparametric estimation of the drift and vola tility are derived. A prior truncation is also useful to eliminate in pract ice the specific dynamics of extreme risks. (C) 2001 Published by Elsevier Science S.A.