Parametric estimation for non recurrent diffusion processes

We consider the trajectory fitting estimators (TFEs) of a parameter in the drift coefficient of a non-recurrent diffusion processes introduced by Keller et al. (1984). We show the strong consistence and Gaussian limit distribution of the TFEs when one continuously observes a sample path over a time interval and obtain rate of convergence greater-order than the standard case. These results extend Dietz (2001) and Dietz and Kutoyants (2003) results in linear and polynomial cases. Numerical simulations illustrate the behavior of the estimators.