Parametric estimation for partially hidden diffusion processes sampled at discrete times

For a one-dimensional diffusion process , we suppose that X(t) is hidden if it is below some fixed and known threshold [tau], but otherwise it is visible. This means a partially hidden diffusion process. The problem treated in this paper is the estimation of a finite-dimensional parameter in both drift and diffusion coefficients under a partially hidden diffusion process obtained by a discrete sampling scheme. It is assumed that the sampling occurs at regularly spaced time intervals of length hn such that nhn=T. The asymptotic is when hn-->0, T-->[infinity] and as n-->[infinity]. Consistency and asymptotic normality for estimators of parameters in both drift and diffusion coefficients are proved.