Recursive Estimation in Diffusion Model

This paper is concerned with the nonlinear identification of dynamical systems disturbed by white noise, an important problem in control engineering. A nonparametric identification procedure for such systems which are usually described by a diffusion model is given in Banon (1977), (1978), where weak consistency of estimators has been obtained and simulation study has been carried out successfully. In this paper, we prove a stronger result concerning asymptotic properties of the estimators of the drift term, namely, strong consistency, and also related results.